# NCERT Solutions Class 8 Maths Chapter 6 Exercise 6.4

Mathematics is a subject that many students are afraid of. It can be extremely difficult to excel in this subject, particularly for students in Class 8. The CBSE Class 8 curriculum for Mathematics includes a number of complex topics that are very challenging for students to comprehend. To perform well on exams, students must have a thorough understanding of the material and regular practice. In exams, students frequently make mistakes that they could have avoided. They occasionally lose marks for not writing thorough answers that follow all the steps. However, students can earn maximum marks for the questions if they have the proper materials and sufficient practice. The Extramarks platform can be of assistance at that point. Students do not have to worry about looking for the appropriate resources because Extramarks offers a 360-degree solution for all of their preparation needs. In Class 8, students are introduced to a lot of new concepts. Some of these are initially challenging to comprehend. However, students can more easily comprehend each topic with the aid of the 3D graphics offered by Extramarks. They can learn all the concepts required by the CBSE curriculum as well as practice questions by using the chapter-by-chapter worksheets and practice questions offered by Extramarks. Along with various study materials, students can also find the NCERT solutions for Mathematics, like the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, to be thorough with the subject.

The Central Board of Secondary Education (CBSE) is a well-known national-level board of school education in India. The CBSE is India’s largest educational board when measured by the total number of enrolled students. Since it is a national-level board, it has affiliations with numerous public and private schools across the nation. The Central Government established the CBSE before the country gained its independence to provide secondary education to students across the country. The board underwent a reorganisation in 1962 to assist students who had to move between states to finish their education requirements. The CBSE affiliates with thousands of schools across the country. In addition, the board is affiliated with a number of institutions outside of India. The board has its national headquarters in New Delhi and regional offices all over the country. The CBSE conducts the board exams for students in Classes 10 and 12.

Class 8 is a crucial and difficult year in a student’s academic career. It gets students ready for the challenging concepts they will study in Class 9 and higher classes. Additionally, it affects the path that students take in their future academic endeavours. Class 8 includes multiple exams and assessments for students to thoroughly understand the concepts they learn. Therefore, in order to succeed at their highest level on all these tests, students need a sound strategy. The future careers of students are directly impacted by their performance in Class 8. The examinations in Class 8 test students’ knowledge of various subjects as well as a variety of soft skills, including perseverance, diligence, intelligence, problem-solving capabilities, stress management abilities, etc. To succeed, students should focus and remain calm as they study for their exams. Avoiding excessive distractions and organising their study time wisely are two things that students should do to score well in the examinations. Along with that, they need access to all the necessary study materials that can help them perform well on the exams. That is why Extramarks provides various study materials for Class 8 students, including the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4.

NCERT exercises are the most important tool for practising questions for the final exams. Additionally, students also need the correct answers to the questions, so they can evaluate their responses. Students can thus get the help they need as they prepare for their exams due to the NCERT solutions. They will be able to apply the chapter’s concepts in a more concise and accurate way by using the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. The comprehensive and error-free NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, have been created by highly experienced teachers. They create these solutions while taking into account the comprehension abilities of Class 8 students. To make writing answers for the problems in this exercise simpler, the problems have been split into smaller, more manageable parts. Examiners frequently stress the need for thorough, step-by-step responses in exams. For the best results, students should adhere to the guidelines in the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4.

**NCERT Solutions for Class 8 Maths Chapter 6- Squares and Square Roots Exercise 6.4**

The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, are available in PDF format on the Extramarks website and mobile application. Students can download the PDF document as well for future practice. By doing so, they can also attempt the NCERT questions and look over their solutions even when they are not online. For complete and thorough exam preparation, they can also find a variety of other study materials on the Extramarks website and mobile app.

**Access NCERT Solutions for Mathematics Chapter 6 – Squares and Square Roots Exercise 6.4**

Students should practice the NCERT textbook questions every day if they want to complete the exam paper in the allotted time. Students’ writing speeds increase as a result of consistent question practice. Questions from the NCERT textbooks are also included on the exam paper. In order to finish the test’s question paper quickly, students should have access to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. They can then learn how to organise their answers and finish more questions.

**Maths NCERT Solutions Class 8 Chapter 6 Exercise 6.4**

Class 8 Maths Chapter 6 Exercise 6.4, covers several important topics such as Finding Square Roots by Division Method, Square Roots of Decimals, and Estimating Square Roots. These topics are essential to learning to find the square root of a number. Students should learn and follow all the methods step by step to be able to solve questions based on these topics. Along with that, they need to practice as many questions as possible. Students need access to a variety of questions and well-written solutions before they appear for their exams. Most question banks base their content primarily on the exercises and examples from NCERT textbooks. It is simpler for students to respond to questions when they have access to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. It helps them understand the topics more quickly. A student feels more prepared for the examinations and gains confidence in grasping the concepts more quickly. This gives them more time to study while maintaining their mental focus on other facets of their education. Understanding the topics covered in the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, will help students advance in their studies. Having access to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, which is adjusted to students’ needs, can be a helpful study aid, despite the fact that the chapter’s content can occasionally be difficult and perplexing. Using these study tools will make learning the concepts related to square roots much easier. Students who want to progress in their preparation should consider practising with the NCERT questions. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, by Extramarks, focus on a particular chapter. For students who want to do better on their exams, there are many study resources available at Extramarks, including chapter-wise worksheets, mock tests and important questions. This makes Extramarks the one-stop destination for studying, practising, and testing. As Extramarks’ NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 are written and edited by subject specialists, all students are ensured of a smooth educational experience.

One of the most crucial tasks for students preparing for the Class 8 exams is to complete the NCERT textbook exercises in Chapter 6. Students should take a few helpful steps when attempting to solve the problems in this chapter for maximum effectiveness. Exams in Mathematics require students to write detailed answers outlining each of the procedures used. Students should therefore be aware of the procedures to follow when writing answers in order to receive full marks for the questions. Firstly, they should carefully read and comprehend the theory in Chapter 6 of the NCERT textbook. Students can use the study materials provided by Extramarks if they are having trouble comprehending the theories. They should attempt the NCERT examples once they have a basic understanding of the material. They should learn all the steps used for finding the answers to the questions. Furthermore, they should learn various methods of finding squares and square roots. Then, they should try to respond to the questions in the exercise one by one. Before referring to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, they should attempt to find the answers on their own. They should try to remember all possible approaches to the problems in order to solve them. They should check the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, to make sure their answers are accurate after trying to answer each question. Using the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, they should correct their inaccurate responses. They must accurately follow the instructions provided in the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. They must attempt to practice these problems repeatedly until they can do so successfully. To find the answers to the questions they are unable to answer, they should also refer to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. They should retry the exercises in the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, once again after looking at the solutions. They will be able to understand the questions better and, as a result, respond to them more quickly. Moreover, they need to make an effort to find solutions as quickly as possible. By answering these types of questions in the examinations more quickly, they would be able to finish the exam paper on time.

**Advantages of CBSE Maths NCERT Solutions Class 8 Chapter 6 Exercise 6.4**

The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 on Extramarks can be advantageous to students in a variety of ways. The comprehensive, stepwise solutions provided by Extramarks in the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 can be used to help students with challenging problems. Complex questions need to be segmented in order to solve them with ease. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 provide the solution to this problem. When students use the NCERT textbook, their understanding of some of the most challenging concepts improves. Students can also evaluate themselves and their progress by comparing their answers to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. On Extramarks, students can find the thoroughly examined NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. Despite the fact that numerous websites are offering these solutions, their accuracy is still in question. Due to the significance of the Class 8 exams, students must use trustworthy study materials. Users have confirmed the validity of the solutions that Extramarks offers. The detailed NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 are presented in clear and understandable language. The most integrated approach for organising answers is given to the students. They provide the simplest and most efficient answers to a variety of mathematical problems.

The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, are regarded as an essential study resource for Class 8 students as they make preparations for the annual exams. The CBSE suggests the NCERT Mathematics textbook for Class 8 students. The NCERT textbook is also recommended in many other boards’ syllabuses. Students from other boards as well as those from the CBSE will benefit from using the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, from Extramarks. Squares and Square Roots are a crucial part of competitive exams like the Olympiad in addition to the annual exams for Class 8 students. A student’s career is significantly impacted by the results of these exams. Students experience so much stress while studying for multiple exams that it exhausts them and occasionally leads them to lose motivation. However, using the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 offered by Extramarks while studying can help students fully comprehend and retain the concepts. As a result, they are more self-assured as they attempt to prepare for multiple exams. For those who thoroughly practice the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, passing the competitive exams will require less effort. To help students pass such difficult exams, the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, provide in-depth explanations of all the solutions. By using the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, they can strengthen their foundational skills. Therefore, the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, are very important, whether preparing for the annual exams or some other competitive examination.

Extramarks provides correct answers to all of the questions in Exercise 6.4 Class 8 Maths. One of the most useful resources for students preparing for the annual exams is the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 offer clear and simple explanations for all of the questions. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 were written and approved by experts with decades of experience. They are completely accurate, faultless, and very dependable. In order to help students achieve the highest marks in their exams, the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 strictly adhere to the CBSE guidelines.

Every detail has been thoroughly explained to aid students in comprehending the concepts. Harder problems have been broken down into smaller parts to make them easier to solve and find the answer. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, include diagrams whenever necessary to aid students in comprehending the solutions. As a result, students can always turn to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, for reliable answers to all of the exercises’ questions.

NCERT textbooks are essential for learning to answer questions. Another advantage of doing so is that the CBSE itself advises using the NCERT textbook for Mathematics. The NCERT books are part of the CBSE’s curriculum. The textbooks contain many significant and exam-relevant problems. These problems frequently trouble students, which undermines their confidence in the subject and the topic. It is crucial to comprehend the concepts of every topic. Students who have access to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, will benefit from having a firm understanding of both basic and advanced concepts when solving the problems presented in the NCERT textbooks. Students who successfully complete it will have a solid conceptual understanding of the chapter. By comparing their own responses to the Extramarks’ provided solutions, they can evaluate their performance and make improvements. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, make it easier to understand the questions by using suitable examples and visuals. It consequently increases students’ self-confidence and aids in their success on the final exam. It enables students to gain a deep understanding of each concept by providing them with enough practice questions for each topic. They can use the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, to improve their theoretical base and receive support throughout their entire study period.

**NCERT Solutions for Class 8**

Students in Class 8 who are studying for their exams can find NCERT solutions for all other exercises and all other subjects in addition to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. The NCERT solutions can be found on both the Extramarks website and the Extramarks mobile app. Understanding the many concepts covered in the CBSE Class 8 curriculum depends on getting the right instruction. It can be difficult to succeed in subjects like Mathematics, and the stress of exams only makes it more difficult. At Extramarks, students can receive NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 from the top subject experts, in addition to using other types of help to fully comprehend the concepts in a particular topic. Students can get the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, from esteemed subject experts by using the carefully created educational materials provided by Extramarks. They can develop optimism in their study plan and prepare for the upcoming tests with the help of subject specialists. A variety of assessments and tests are given in Class 8 at the school level to help students get the necessary knowledge. To succeed in all these exams, however, students require expert help. Exam preparation might be bolstered by having access to NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, from top subject experts.

In addition to the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4, there are additional study resources for Class 8 students available on Extramarks. It is easier to fully comprehend the ideas required to respond to the exercise questions with the help of these study materials. Students can also utilise these study materials to help them revise the topics. Educators who have advanced knowledge and many years of experience present them in a simple manner. Extramarks provides practice worksheets, MCQs, mock tests, past years’ papers, revision notes, CBSE sample question papers, and more. Without looking elsewhere, students can find everything they need in one location and save time. With the help of brief notes and sample question papers, students can quickly review every topic covered in the curriculum prior to exams. The Extramarks Learning App offers chapter-wise worksheets, interactive activities, a large number of practice questions, and much more to guarantee complete mastery of all subjects and topics. They can develop an upward learning curve and assess their understanding by using mock tests and adaptive tests with rising levels of difficulty. Additionally, for help with questions based on Squares and Square Roots, students can obtain the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. This will help them solve all the questions in NCERT Maths Class 8 Chapter 6 Exercise 6.4.

**Q.1 **Find the square root of each of the following numbers by Division method.

(i) 2304 (ii) 4489 (iii) 3481 (iv) 529 (v) 3249 (vi) 1369 (vii) 5776 (viii) 7921 (ix) 576 (x) 1024 (xi) 3136 (xii) 900

**Ans**

\begin{array}{l}\text{(i) Consider}\sqrt{2304}\\ \\ \begin{array}{cc}& 48\\ 4& \begin{array}{l}\text{}\overline{23}\text{}\overline{04}\\ -16\end{array}\\ 88& \begin{array}{l}\text{}704\\ -704\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{2304}=48\\ \\ \text{(ii) Consider}\sqrt{4489}\\ \\ \begin{array}{cc}& 67\\ 6& \begin{array}{l}\text{}\overline{44}\text{}\overline{89}\\ -36\end{array}\\ 127& \begin{array}{l}\text{}889\\ -889\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{4489}=67\end{array}

\begin{array}{l}\text{(iii) Consider}\sqrt{3481}\\ \\ \begin{array}{cc}& 59\\ 5& \begin{array}{l}\text{}\overline{34}\text{}\overline{81}\\ -25\end{array}\\ 109& \begin{array}{l}\text{}981\\ -981\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{3481}=59\\ \\ \text{(iv) Consider}\sqrt{529}\\ \\ \begin{array}{cc}& 23\\ 2& \begin{array}{l}\text{}\overline{5}\text{}\overline{29}\\ -4\end{array}\\ 43& \begin{array}{l}\text{}129\\ -129\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{529}=23\end{array}

\begin{array}{l}\text{(v) Consider}\sqrt{3249}\\ \\ \begin{array}{cc}& 57\\ 5& \begin{array}{l}\text{}\overline{32}\text{}\overline{49}\\ -25\end{array}\\ 107& \begin{array}{l}\text{}749\\ -749\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{3249}=57\\ \\ \text{(vi) Consider}\sqrt{1369}\\ \\ \begin{array}{cc}& 37\\ 3& \begin{array}{l}\text{}\overline{13}\text{}\overline{69}\\ -9\end{array}\\ 67& \begin{array}{l}\text{}469\\ -469\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{1369}=37\end{array}

\begin{array}{l}\text{(vii) Consider}\sqrt{5776}\\ \\ \begin{array}{cc}& 76\\ 7& \begin{array}{l}\text{}\overline{57}\text{}\overline{76}\\ -49\end{array}\\ 146& \begin{array}{l}\text{876}\\ -876\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{5776}=76\\ \\ \text{(viii) Consider}\sqrt{7921}\\ \\ \begin{array}{cc}& 89\\ 8& \begin{array}{l}\text{}\overline{79}\text{}\overline{21}\\ -64\end{array}\\ 169& \begin{array}{l}\text{1521}\\ -1521\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{7921}=89\end{array}

\begin{array}{l}\text{(ix) Consider}\sqrt{576}\\ \\ \begin{array}{cc}& 24\\ 2& \begin{array}{l}\text{}\overline{5}\text{}\overline{76}\\ -4\end{array}\\ 44& \begin{array}{l}\text{176}\\ -176\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{576}=24\\ \\ \text{(x) Consider}\sqrt{1024}\\ \\ \begin{array}{cc}& 32\\ 3& \begin{array}{l}\text{}\overline{10}\text{}\overline{24}\\ -9\end{array}\\ 62& \begin{array}{l}\text{124}\\ -124\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{1024}=32\end{array}

$\begin{array}{l}\text{(xi) Consider}\sqrt{3136}\\ \\ \begin{array}{cc}& 56\\ 5& \begin{array}{l}\text{}\overline{31}\text{}\overline{36}\\ -25\end{array}\\ 106& \begin{array}{l}\text{636}\\ -636\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{3136}=56\\ \\ \text{(xii) Consider}\sqrt{900}\\ \\ \begin{array}{cc}& 30\\ 3& \begin{array}{l}\text{}\overline{9}\text{}\overline{00}\\ -9\end{array}\\ 60& \begin{array}{l}\text{00}\\ 00\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{900}=30\end{array}$ \begin{array}{l}\end{array}

**Q.2** Find the number of digits in the square root of each of the following numbers (without any calculation).

(i) 64 (ii) 144 (iii) 4489 (iv) 27225 (v) 390625

**Ans**

We can find the number of digits in the square root of each of the given numbers by placing bars on them.

(i) By placing bars, we obtain

$64=\overline{64}$

Since there is only one bar, the square root of 64 will have only one digit in it.

(ii) By placing bars, we obtain

$144=\overline{1}\overline{44}$

Here, we have two bars, so the square root of 144 will have 2 digits in it.

(iii) By placing bars, we obtain

$4489=\overline{44}\overline{89}$

Since there are two bars, the square root of 4489 will have 2 digits in it.

(iv) By placing bars, we obtain

$27225=\overline{2}\overline{72}\overline{25}$

Here we have three bars, so the square root of 27225 will have three digits in it.

$390625=\overline{39}\overline{06}\overline{25}$

Here, also we have three bars; the square root of 390625 will have 3 digits in it.

**Q.3 **Find the square root of the following decimal numbers.

(i) 2.56 (ii) 7.29 (iii) 51.84 (iv) 42.25 (v) 31.36

**Ans**

\begin{array}{l}\text{(i) Consider}\sqrt{2.56}\\ \\ \begin{array}{cc}& 1.6\\ 1& \begin{array}{l}\text{}\overline{2}\text{}\text{.}\overline{56}\\ -1\end{array}\\ 26& \begin{array}{l}\text{156}\\ -156\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{2.56}=1.6\end{array}

\begin{array}{l}\text{(ii)Consider}\sqrt{7.29}\\ \\ \begin{array}{cc}& 2.7\\ 2& \begin{array}{l}\text{}\overline{7}\text{}\text{.}\overline{29}\\ -4\end{array}\\ 47& \begin{array}{l}\text{329}\\ -329\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{7.29}=2.7\\ \\ \\ \text{(iii)Consider}\sqrt{51.84}\\ \\ \begin{array}{cc}& 7.2\\ 7& \begin{array}{l}\text{}\overline{51}\text{}\text{.}\overline{84}\\ -49\end{array}\\ 142& \begin{array}{l}\text{284}\\ -284\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{51.84}=7.2\end{array}

\begin{array}{l}\text{(iv)Consider}\sqrt{42.25}\\ \\ \begin{array}{cc}& 6.5\\ 6& \begin{array}{l}\text{}\overline{42}\text{}\text{.}\overline{25}\\ -36\end{array}\\ 125& \begin{array}{l}\text{625}\\ -625\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{42.25}=6.5\\ \\ \\ \text{(v)Consider}\sqrt{31.36}\\ \\ \begin{array}{cc}& 5.6\\ 5& \begin{array}{l}\text{}\overline{31}\text{}\text{.}\overline{36}\\ -25\end{array}\\ 106& \begin{array}{l}\text{636}\\ -636\end{array}\\ & 0\end{array}\\ \\ \therefore \sqrt{31.36}=5.6\end{array}

**Q.4 **Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

(i) 402 (ii) 1989 (iii) 3250 (iv) 825 (v) 4000

**Ans**

\begin{array}{l}\text{(i) Consider}\sqrt{402}\\ \\ \begin{array}{cc}& 20\\ 2& \begin{array}{l}\text{}\overline{4}\text{}\overline{02}\\ -4\end{array}\\ 40& \begin{array}{l}\text{02}\\ 00\end{array}\\ & 2\end{array}\\ \\ \text{Here,the remainder is 2}.\text{Therefore},\text{if we subtract 2 from 402,we}\\ \text{will get a perfect square}\text{.}\\ \text{Therefore},\text{required perfect square}=\text{4}0\text{2}-\text{2}=\text{4}00\\ \therefore \sqrt{400}=20\end{array}

\begin{array}{l}\text{(ii) Consider}\sqrt{1989}\\ \\ \begin{array}{cc}& 44\\ 4& \begin{array}{l}\text{}\overline{19}\text{}\overline{89}\\ -16\end{array}\\ 84& \begin{array}{l}\text{389}\\ 336\end{array}\\ & 53\end{array}\\ \\ \text{Here,the remainder is 53}.\text{Therefore},\text{if we subtract 53 from 1989,we}\\ \text{will get a perfect square}\text{.}\\ \text{Therefore},\text{required perfect square}=1989-53=1936\\ \therefore \sqrt{1936}=44\\ \\ \text{(iii) Consider}\sqrt{3250}\\ \\ \begin{array}{cc}& 57\\ 5& \begin{array}{l}\text{}\overline{32}\text{}\overline{50}\\ -25\end{array}\\ 107& \begin{array}{l}\text{750}\\ 749\end{array}\\ & 1\end{array}\\ \\ \text{Here,the remainder is 1}.\text{Therefore},\text{if we subtract 1 from 3250,we}\\ \text{will get a perfect square}\text{.}\\ \text{Therefore},\text{required perfect square}=3250-1=3249\\ \therefore \sqrt{3249}=57\end{array}

\begin{array}{l}\text{(iv) Consider}\sqrt{825}\\ \\ \begin{array}{cc}& 28\\ 2& \begin{array}{l}\text{}\overline{8}\text{}\overline{25}\\ -4\end{array}\\ 48& \begin{array}{l}\text{425}\\ 384\end{array}\\ & 41\end{array}\\ \\ \text{Here,the remainder is 41}.\text{Therefore},\text{if we subtract 41 from 825,we}\\ \text{will get a perfect square}\text{.}\\ \text{Therefore},\text{required perfect square}=825-41=784\\ \therefore \sqrt{784}=28\\ \\ \text{(v) Consider}\sqrt{4000}\\ \\ \begin{array}{cc}& 63\\ 6& \begin{array}{l}\text{}\overline{40}\text{}\overline{00}\\ -36\end{array}\\ 123& \begin{array}{l}\text{400}\\ 369\end{array}\\ & 31\end{array}\\ \\ \text{Here,the remainder is 31}.\text{Therefore},\text{if we subtract 31 from 4000,we}\\ \text{will get a perfect square}\text{.}\\ \text{Therefore},\text{required perfect square}=4000-31=3969\\ \therefore \sqrt{3969}=63\end{array}

**Q.5 **Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.

(i) 525 (ii) 1750 (iii) 252 (iv) 1825 (v) 6412

**Ans**

\begin{array}{l}\text{(i) Consider}\sqrt{525}\\ \\ \begin{array}{cc}& 22\\ 2& \begin{array}{l}\text{}\overline{5}\text{}\overline{25}\\ -4\end{array}\\ 42& \begin{array}{l}\text{125}\\ 84\end{array}\\ & 41\end{array}\\ \\ \text{Here,the remainder is 41}.\text{}\text{}\text{This means that square of 22 is less than 525}\text{.}\\ \text{The next number is 23 and the square of 23 is 529}\text{.}\\ \\ {\text{Hence, the number to be added to 525 = 23}}^{\text{2}}-525=529-525=4\\ \\ \text{Therefore},\text{required perfect square}=525+4=529\\ \therefore \sqrt{529}=23\end{array}

\begin{array}{l}\text{(ii) Consider}\sqrt{1750}\\ \\ \begin{array}{cc}& 41\\ 4& \begin{array}{l}\text{}\overline{17}\text{}\overline{50}\\ -16\end{array}\\ 81& \begin{array}{l}\text{150}\\ 81\end{array}\\ & 69\end{array}\\ \\ \text{Here,the remainder is 69}.\text{}\text{}\text{This means that square of 41 is less than 1750}\text{.}\\ \text{The next number is 42 and the square of 42 is 1764}\text{.}\\ {\text{Hence, the number to be added to 1750 = 42}}^{\text{2}}-1750=1764-1750=14\\ \text{Therefore},\text{required perfect square}=1750+14=1764\\ \therefore \sqrt{1764}=42\\ \\ \text{(iii) Consider}\sqrt{252}\\ \\ \begin{array}{cc}& 15\\ 1& \begin{array}{l}\text{}\overline{2}\text{}\overline{52}\\ -1\end{array}\\ 25& \begin{array}{l}\text{152}\\ 125\end{array}\\ & 27\end{array}\\ \\ \text{Here,the remainder is 27}.\text{}\text{}\text{This means that square of 15 is less than 252}\text{.}\\ \text{The next number is 16 and the square of 16 is 256}\text{.}\\ {\text{Hence, the number to be added to 252 = 16}}^{\text{2}}-252=256-252=4\\ \text{Therefore},\text{required perfect square}=252+4=256\\ \therefore \sqrt{256}=16\end{array}

\begin{array}{l}\text{(iv) Consider}\sqrt{1825}\\ \\ \begin{array}{cc}& 42\\ 4& \begin{array}{l}\text{}\overline{18}\text{}\overline{25}\\ -16\end{array}\\ 82& \begin{array}{l}\text{225}\\ 164\end{array}\\ & 61\end{array}\\ \\ \text{Here,the remainder is 61}.\text{}\text{}\text{This means that square of 42 is less than 1825}\text{.}\\ \text{The next number is 43 and the square of 43 is 1849}\text{.}\\ {\text{Hence, the number to be added to 1825 = 43}}^{\text{2}}-1825=1849-1825=24\\ \text{Therefore},\text{required perfect square}=1825+24=1849\\ \therefore \sqrt{1849}=43\\ \\ \text{(v) Consider}\sqrt{6412}\\ \\ \begin{array}{cc}& 80\\ 8& \begin{array}{l}\text{}\overline{64}\text{}\overline{12}\\ -64\end{array}\\ 160& \begin{array}{l}\text{012}\\ 0\end{array}\\ & 12\end{array}\\ \\ \text{Here,the remainder is 12}.\text{}\text{}\text{This means that square of 80 is less than}6412.\\ \text{The next number is 81 and the square of 81 is 6561}\text{.}\\ \text{Hence, the number to be added to}6412{\text{= 81}}^{\text{2}}-6412=6561-6412=149\\ \text{Therefore},\text{required perfect square}=6412+149=6561\\ \therefore \sqrt{6561}=81\end{array}

**Q.6** Find the length of the side of a square whose area is 441 m^{2}.

**Ans**

$\begin{array}{l}\text{Let the length of the side of the square be}\mathrm{x}\text{metres.}\\ \text{Area of the square}=441\text{}{\mathrm{m}}^{2}\text{}\\ \text{i.e.}{\mathrm{x}}^{2}=441\text{}{\mathrm{m}}^{2}\text{}\\ \Rightarrow \mathrm{x}=\sqrt{441}\\ \\ \text{The square root of 441 can be obtained as follows:}\\ \begin{array}{cc}& 21\\ 2& \begin{array}{l}\text{}\overline{4}\text{}\overline{41}\\ -4\end{array}\\ 41& \begin{array}{l}\text{41}\\ 41\end{array}\\ & 0\end{array}\\ \\ \therefore \mathrm{x}=21\text{m}\\ \text{Therefore},\text{the length of the side of the square be}21\text{metres.}\end{array}$

**Q.7 **In a right triangle ABC, ∠B = 90°.

(a) If AB = 6 cm, BC = 8 cm, find AC (b) If AC = 13 cm, BC = 5 cm, find AB.

**Ans**

(a) Given: AB = 6 cm, BC = 8 cm and ΔABC is right-angled at B.

Therefore, by applying Pythagoras theorem, we obtain

\begin{array}{l}{\text{AC}}^{\text{2}}={\text{AB}}^{\text{2}}+{\text{BC}}^{\text{2}}\\ \Rightarrow {\text{AC}}^{\text{2}}={\left(\text{6 cm}\right)}^{\text{2}}+{\left(\text{8 cm}\right)}^{\text{2}}\\ \Rightarrow {\text{AC}}^{\text{2}}=\left(\text{36}+\text{64}\right){\text{cm}}^{\text{2}}=\text{1}00{\text{cm}}^{\text{2}}\\ \Rightarrow \text{AC}=\sqrt{\text{1}00\text{}}\text{cm}=\text{10 cm}\\ \therefore \text{AC}=\text{10cm}\end{array}

(b) Given: AC = 13 cm, BC = 5 cm and ΔABC is right-angled at B.

Therefore, by applying Pythagoras theorem, we obtain

\begin{array}{l}{\text{AC}}^{\text{2}}={\text{AB}}^{\text{2}}+{\text{BC}}^{\text{2}}\\ \Rightarrow {\left(\text{13cm}\right)}^{\text{2}}={\left(\text{AB}\right)}^{\text{2}}+{\left(\text{5 cm}\right)}^{\text{2}}\\ \Rightarrow {\text{AB}}^{\text{2}}=\left(\text{13}-5\right){\text{cm}}^{\text{2}}\\ \Rightarrow {\text{AB}}^{\text{2}}=\left(169-25\right){\text{cm}}^{\text{2}}=144{\text{cm}}^{\text{2}}\\ \Rightarrow \text{AB}=\sqrt{144}\text{cm}=\text{12 cm}\\ \therefore \text{AB}=\text{12 cm}\end{array}

**Q.8 **A gardener has 1000 plants. He wants to plant these in such a way that the number of rows and the number of columns remain same. Find the minimum number of plants he needs more for this.

**Ans**

It is given that the gardener has 1000 plants. The number of rows and the number of columns is the same.

We have to find the number of plants that should be more planted such that the number of rows and columns are same.

That means we have to find the number which should be added to 1000 to make it a perfect square

The square root of 1000 can be calculated as follows:

\begin{array}{l}\begin{array}{cc}& 31\\ 3& \begin{array}{l}\text{}\overline{10}\text{}\overline{00}\\ -9\end{array}\\ 61& \begin{array}{l}\text{100}\\ 61\end{array}\\ & 39\end{array}\\ \\ \text{The remainder is 39}.\text{It represents that the square of 31 is less than 1}000.\\ \text{The next number is 32 and the square of 32}=\text{1}0\text{24}\text{.}\\ \\ \text{Hence},\text{number to be added to 1}000\text{to make it a}\\ \text{perfect square}={\text{32}}^{\text{2}}-\text{1}000=\text{1}0\text{24}-\text{1}000=\text{24}\\ \text{Thus},\text{the required number of plants is 24}.\\ \end{array}

**Q.9 **There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement?

**Ans**

It is given that there are 500 children in the school. They have to stand for a P.T. drill such that the number of rows is equal to the number of columns.

We have to find the number of children who will be left out in this arrangement.

That means we have to calculate the number which should be subtracted from 500 to make it a perfect square.

The square root of 500 can be calculated by long division method as follows.

\begin{array}{cc}& 22\\ 2& \begin{array}{l}\text{}\overline{5}\text{}\overline{00}\\ -4\end{array}\\ 42& \begin{array}{l}\text{100}\\ 84\end{array}\\ & 16\end{array}

$\begin{array}{l}\text{The remainder is 16}.\text{}\\ \therefore \text{the number to be subtracted from 500 to make it a}\\ \text{perfect square}=16\\ \text{So, the required number is}500-16=484\\ \text{Thus, the number of children who will be left out is 16}\text{.}\end{array}$

##### FAQs (Frequently Asked Questions)

## 1. Where are the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 available for Class 8 students to access?

On the Extramarks website and mobile application, Class 8 students can access the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. It is simple to download the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 in PDF format from the Extramarks website and mobile application for year-round access.

## 2. Are questions from the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 included in the Class 8 examinations?

The Extramarks-provided NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 are extremely important in terms of exams. Many of these questions appear frequently in exams. They are based on some of the chapter’s key concepts and are likely to appear in Class 8 exams.

## 3. How many questions are resolved in the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 offered by Extramarks?

The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 provide answers for all nine questions in Square And Square Roots Class 8 Exercise 6.4. Students can find all the steps necessary to solve the questions in the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 offered by Extramarks in order to get the best possible grade on the exam.

## 4. Can one finish the Mathematics question paper in the allotted time by practising the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 before the exam?

Practising the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 can help students gain an understanding of the question types as well as help identify various important questions. The ability to answer questions more quickly can be improved with more practice with the NCERT exercises. By doing that, students will eventually be able to complete the entire Mathematics exam question paper within the allotted time.

## 5. How should students use the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 when studying for the final exams?

Students should carefully read through each concept in the chapter from the NCERT book before moving on. Afterwards, they should go over the examples from the textbook. They will learn different methods for solving the questions in this chapter as a result of this. They should try the exercises’ questions after finishing all the examples. Not only that, but they must attempt to solve the questions without taking the aid of NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4. When they are finished, they can use the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.4 to verify their answers. They must correct their mistakes and fully grasp the methods described in the solutions if they are to successfully solve the problems. They should then attempt to solve the exercises’ questions once more to determine their progress. Furthermore, they will be able to comprehend the chapter’s material better and, as a result, score higher on the Mathematics exam.