# NCERT Solutions Class 8 Maths Chapter 6 Exercise 6.1

The eighth grade is considered one of the most important points in a student’s academic career. Students must understand all the fundamentals in the curriculum of this class in order to do well in the senior classes and earn higher grades. It is an extremely important academic milestone for a student because they learn all the fundamental ideas that they will need in their subsequent classes. Students in Class 8 should be familiar with the fundamentals of each subject because the curricula of the senior classes will cover the same material but in more detail.

A multitude of subjects is covered by the curriculum for the academic year of Class 8. In order to advance to the next class, Class 8 students must complete the syllabus of all required subjects. The Class 8 CBSE syllabus for each subject will aid students in understanding what they will study during the designated academic year.

The syllabus, created by the CBSE board in accordance with a comprehensive framework, will assist Class 8 students in effectively preparing for their exams. Students can prepare effectively for their exams and earn higher grades with the help of Class 8 study materials for the CBSE Board. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 were created following the CBSE Board’s most recent Class 8 syllabus. Since most of the questions on the final exam are taken from textbooks, NCERT textbooks are a crucial study tool for Class 8 students.

The academic curriculum of senior classes is grounded in the principles and ideas students learn in Class 8. As a result, students in Class 8 are required to approach their studies methodically. The courses, syllabus, and examination schedule must all be carefully studied in order to accomplish this. In order to assist students, the CBSE has developed a thorough syllabus for Class 8 that covers all academic subjects.

NCERT Class 8 solutions are a valuable tool for comprehending themes in Mathematics and Science, and they can help students effectively prepare for their Class 8 term and annual exams. With this purpose in mind, Extramarks has compiled comprehensive Maths and Science NCERT solutions for Class 8. Highly qualified academic experts and educators from Extramarks have carefully crafted the NCERT Solutions for Class 8 in the disciplines of Mathematics and Science.

The Class 8 curriculum serves as the foundation for senior classes, so students should concentrate on their studies in this class. The Class 8 curriculum is closely related to the curricula of classes 9 and 10. Therefore, every concept covered in the NCERT Class 8 textbooks must be understood by every Class 8 student. Extramarks is giving students access to NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, in PDF format to aid their preparation for the examination.

When preparing for the Class 8 CBSE exams, students are often inhibited by the academic discipline of Mathematics. However, students who enjoy playing with numbers view Mathematics as enjoyable. A proper commitment is necessary to achieve better grades, but good grades themselves are not a problem. Since Mathematics is entirely based on numbers, it is not a language-based subject. Students either get the answer correct or incorrect, allowing them to earn full marks in this subject. The right preparation will undoubtedly help them achieve excellence in the Mathematics subject. Mathematics is not a subject that can be mastered in a single day. The subject fosters in students the development of logical thinking and an approach to problem solving.

The BODMAS rule, which holds the secret to the right response, should be understood. The abbreviation BODMAS stands for Bracket of Division, Multiplication, Addition, and Subtraction. A student’s ability to solve problems quickly and efficiently during the exam will depend on whether the fundamentals are covered. Students should make a list of key ideas, formulas, and other important themes to retain while studying NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. By doing this, students will be able to overcome obstacles to learning more quickly and with less effort. As everyone is aware, the only certain way to succeed in any exam is to practice constantly.

As a result, students must thoroughly practice exercise questions using the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. Since CBSE incorporates the NCERT textbooks in its curriculum, it is necessary to finish reading the NCERT textbooks first before moving on to other practice sets. When students are finished with the NCERT textbooks, they should make sure to review the test questions from past years. Solving past years’ papers will help students understand the types of questions and the difficulty level being asked in the examination.

By working through past years’ papers, students can get ready for the Class 8 annual exams by adhering to an ideal strategy. To succeed in Class 8 annual exams, students must analyse their performance in addition to planning and practising papers. Regularly reviewing their study materials will enable them to strengthen their weak areas and ace the exam. All of their questions pertaining to specific subjects would also be answered.

The importance of each topic and subtopic must be fully understood by the student after carefully reading each chapter. It is essential to comprehend the core ideas of each chapter in order to prepare the chapters effectively. The most effective way to learn the fundamentals of Mathematics is through problem-solving. Students must first answer the straightforward questions before moving on to the more difficult ones. All students must thoroughly prepare for the annual exams. Before preparing for the Mathematics examination, students should become acquainted with the CBSE syllabus. A learning strategy for the chapters of Mathematics must be developed using the syllabus.

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Knowledge of the scheme of mark distribution and topic weightage is essential for students to perform well on their final exams. One of the best ways to comprehend the appropriate marking schemes is by using sample papers. Often, students do not organise a productive study schedule to get ready for exams. Students must devote sufficient time to each of the assigned topics. When studying for their annual exams, students should keep in mind that they will last three hours. Moreover, it is advised that students attempt the questions with 1 and 2 marks last and always begin with the questions with higher scores.

Chapter 6 of the curriculum of Mathematics for Class 8 could be challenging for students. Practising is very important for understanding the application of formulas. This chapter contains a good number of exercises for helping students clear their doubts about this chapter in depth. Notably, many students may be facing some challenges while solving the practice. So Extramarks is one of the best platforms for accessing the solutions for Class 8 Maths Chapter 6 Exercise 6.1.

Students can solve and practise a vast number of questions in the NCERT textbook. Students should start practising with the aid of NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 which will help students achieve good marks in their Class 8 annual exams. Students having difficulties with Chapter 6 should seek assistance from NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 Students can easily access the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 on the Extramarks website and mobile application.

**NCERT Solutions for Class 8 Maths Chapter 6 Squares and Square Roots (EX 6.1) Exercise 6.1 **

Extramarks website and mobile application make it simple to access NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. Using the best study materials when students start preparing for the Mathematics examination streamlines the process. Students who study the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, find it easier to learn all the designated themes. It allows them to assess their preparation for concepts they have already learned in less time. They also save time, even though they do not have to learn from textbooks.

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There are several exercises in Chapter 6, which have varying levels of complexity. Many students became puzzled while attempting to solve the exercises of Chapter 6. Students can use the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 to help them with their practice. Students can find the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 on the Extramarks website and mobile application.

**Access NCERT Solutions for Class 8 Maths Chapter 6 – Squares and Square Roots Exercise 6.1**

Extramarks’ solutions for Class 8 Chapter 6 titled Square and Square Roots, were created following the most recent syllabus and strict adherence to CBSE board guidelines. Students must review the solutions and any accompanying notes in order to comprehend the concepts. The NCERT solutions for Chapter 6 are available in PDF format for download from the Extramarks website. On Extramarks, students can find NCERT solutions for a variety of subjects and grade levels. If students require additional assistance with any subject, they could interact with mentors of Extramarks.

The various methods for determining whether a given natural number is a perfect square number or not are covered in this chapter. The characteristics and patterns that square numbers follow serve as examples of these methods. The various techniques for locating square numbers and square roots are also covered in this chapter. Understanding the idea of square roots will be simple if students are familiar with exponents. Before dealing with Chapter 6 NCERT solutions, students should take a moment to quickly review the chapter.

The Mathematics annual exam requires practice to be passed successfully. At regular intervals, students must practise exercise questions from each chapter of Class 8 Mathematics. When preparing for the Mathematics exam, the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, are essential tools. Students enrolled in Hindi-medium educational institutions affiliated with the Central Board of Secondary Education can access the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, in PDF format via the Extramarks website and mobile application. All answers are provided by subject experts in Mathematics. Students can efficiently solve all of the questions in the Class 8 Mathematics chapters with the help of the Class 8 Maths NCERT Solutions.

Students in Class 8 of the Central Board of Secondary Education must visit the Extramarks website and mobile application to access the Class 8 Maths solutions. The Class 8 Maths NCERT solutions are in PDF format, so students can use them without requiring access to the internet. Students should make a list of all challenging questions in an exercise and solve them using the Maths NCERT solutions. Maths NCERT solutions are available for all chapters.

**2. Give reason why the following numbers are not perfect squares.**

There are a lot of worthwhile exercises in this chapter that help students fully grasp the material. Students can easily find the answers to the questions contained in Exercise 6.1 in NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. The best study tool is NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, which will help students understand formulas and chapters. If they practice consistently and allow enough time for each topic, students can quickly learn the formulas.

**3. Find the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.**

Students can take help from the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 to solve the Square And Square Roots Class 8 Exercise 6.1. In NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, students find all the answers in easy and simple language to understand the solution to the questions easily.

**4. Find the missing digits after observing the following pattern.**

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**5. Find the missing number after observing the following pattern.**

Chapter 6 is very vast and has a lot of formulas. It is very important to understand them completely to get the best marks in the examination. Getting the desired marks in Mathematics requires a lot of practice. The only way to understand a chapter deeply in Mathematics is through practice.

**6. Find the missing numbers using the given pattern.**

In this chapter, there are many exercises that help students understand the chapter perfectly. Finding the missing numbers using the given pattern is a pertinent question in the designated exercise. Accordingly, students can easily find out the answer to this question in NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1.

**7. Find the sum without adding.**

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**9. How many numbers lie between squares of the following numbers?**

The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, have all the answers to Exercise 6.1 in the NCERT Textbook. Moreover, students can take help in solving the question from NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. This chapter requires proper practice and understanding of all the formulas, and it is best to practice with NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1.

**NCERT Solution Class 8 Maths Chapter 6 Other Exercises**

Extramarks’ NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 for the chapter on Square and Square Roots are created following the most recent curriculum and strictly adhere to the guidelines established by the CBSE board. Students must review the solutions and accompanying notes to comprehend the concept. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, are available in an accessible PDF format for download from the Extramarks website. On Extramarks, students can find NCERT solutions for various subjects and grade levels.

The various methods for determining whether a given natural number is a perfect square number or not are covered in this chapter. The characteristics and recurring patterns of square numbers serve as examples of these strategies. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 should be reviewed quickly by students before attempting the exercise.

**Benefits of NCERT Solutions for Class 8 Maths Chapter 6**

The solutions Extramarks offers are written in the most straightforward style, and students learn the terms in understandable language. There is a good chance that students will achieve high grades if they use the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. Extramarks provide solutions to mathematical problems equipped with examples to descriptively explain the specifics of the solution.

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**NCERT Solutions for Class 8**

The best resources for studying for the Mathematics exam are the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. Students of Class 8 and other classes can access NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, in PDF format. The NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1, are easy to download and accessible offline. Extramarks subject experts and qualified teachers created these materials following the most recent syllabus. Students will face no hindrances while preparing for their exams with the help of these materials and will achieve top grades. These resources are always available for Class 8 students to use at their convenience. They can quickly review all the critical ideas with the help of revision notes, and the best approaches to answering the questions will be provided in the solutions. In order to improve their knowledge of a topic, students can also use NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 to practice more questions and better understand the question format.

**Q.1 **What will be the unit digit of the squares of the following numbers?

(i) 81 (ii) 272 (iii) 799 (iv) 3853 (v) 1234 (vi) 26387 (vii) 52698 (viii) 99880 (ix) 12796 (x) 55555

**Ans**

- 81- Here, the number ends with 1.So its square will end with (1×1=1).Therefore, the unit digit of the square of 81 will be 1.
- 272 – Here, the number ends with 2.So its square will end with (2×2=4).Therefore, the unit digit of the square of 272 will be 4.
- 799 – Here, the number ends with 9.So its square will end with (9×9= 81).Therefore, the unit digit of the square of 799 will be 1.
- 3853- Here, the number ends with 3.So its square will end with (3×3=9).Therefore, the unit digit of the square of 3853 will be 9.
- 1234 – Here, the number ends with 4. So its square will end with (4×4=16).Therefore, the unit digit of the square of 1234 will be 6.
- 26387- Here, the number ends with 7. So its square will end with (7×7=49).Therefore, the unit digit of the square of 23387 will be 9.
- 52698 – Here, the number ends with 8. So its square will end with (8×8=64).Therefore, the unit digit of the square of 52698 will be 4
- 99880- Here, the number ends with 0. So its square will end with (0×0=0).Therefore, the unit digit of the square of 99880 will be 0.
- 12796 – Here, the number ends with 6. So its square will end with (6×6=36).Therefore, the unit digit of the square of 12796 will be 6.
- 55555- Here, the number ends with 5. So its square will end with (5×5=25). Therefore, the unit digit of the square of 55555 will be 5.

**Q.2** The following numbers are obviously not perfect squares. Give reason.

(i) 1057 (ii) 23453 (iii) 7928 (iv) 222222 (v) 64000 (vi) 89722 (vii) 222000 (viii) 505050

**Ans**

A perfect square of any number ends with any of the digits 0, 1,4,5,6 or 9 at its unit’s place. Also, a perfect square will end with even number of zeroes.

- 1057: Since the unit digit of 1057 is 7.Therefore, it is not a perfect square.
- 23453: Since the unit digit of 23453 is 3.Therefore, it is not a perfect square.
- 7928: Since the unit digit of 7928 is 8.Therefore, it is not a perfect square.
- 222222: Since the unit digit of 222222 is 2. Therefore, it is not a perfect square.
- 64000: A perfect square should have even number of zeroes at the end but 64000 is having three zeroes at the end which is not an even number. Therefore, it is not a perfect square.
- 89722 : Since the unit digit of 89722 is 2.Therefore,it is not a perfect square.
- 222000 : A perfect square should have even number of zeroes at the end but 222000 is having three zeroes at the end which is not an even number. Therefore, it is not a perfect square.
- A perfect square should have even number of zeroes at the end but 505050 is having one zero at the end which is not an even number. Therefore, it is not a perfect square.

**Q.3 **The squares of which of the following would be odd numbers?

(i) 431 (ii) 2826 (iii) 7779 (iv) 82004

**Ans**

Here, 431 and 7779 are odd numbers and 2826 and 82004 are even numbers

We know that the square of an odd number is odd and the square of an even number is even.

Thus, the squares of 431 and 7779 will be odd numbers.

**Q.4 **Observe the following pattern and find the missing digits.

11^{2} = 121

101^{2} = 10201

1001^{2} = 1002001

100001^{2} = 1 ……… 2 ……… 1

10000001^{2} = ………………………

**Ans**

We can observe that, the squares of the given numbers have the same number of zeroes before and after the digit 2 as it was in the original number. Therefore,

100001^{2} = 10000200001

10000001^{2} = 100000020000001

**Q.5** Observe the following pattern and supply the missing numbers.

11^{2} = 1 2 1

101^{2} = 1 0 2 0 1

10101^{2} = 102030201

1010101^{2} = ………………………

…………^{2} = 10203040504030201

**Ans**

We can observe that, the squares of the given numbers have the same number of zeroes after every digit as it was in the original number.

Therefore,

1010101^{2 }= 1020304030201

101010101^{2} = 10203040504030201

Hence, the missing numbers are:

1020304030201, 101010101^{2}

**Q.6 **Using the given pattern, find the missing numbers.

1^{2} + 2^{2} + 2^{2} = 3^{2}

2^{2} + 3^{2} + 6^{2} = 7^{2}

3^{2} + 4^{2} + 12^{2} = 13^{2}

4^{2} + 5^{2} + _^{2} = 21^{2}

5^{2} + _^{2} + 30^{2} = 31^{2}

6^{2} + 7^{2} + _^{2} = __^{2}

**Ans**

Clearly, the third number is the product of the first two numbers and the fourth number can be obtained by adding 1 to the third number.

Thus, the missing numbers in the pattern will be as follows.

\begin{array}{l}{\text{4}}^{\text{2}}+{\text{5}}^{\text{2}}+\underset{\xaf}{{20}^{2}}={\text{21}}^{\text{2}}\\ {\text{5}}^{\text{2}}+\underset{\xaf}{{6}^{2}}+\text{3}{0}^{\text{2}}={\text{31}}^{\text{2}}\\ {\text{6}}^{\text{2}}+{\text{7}}^{\text{2}}+\underset{\xaf}{{42}^{2}}=\underset{\xaf}{{43}^{2}}\end{array}

**Q.7 **Without adding, find the sum.

(i) 1 + 3 + 5 + 7 + 9

(ii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 +19

(iii) 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21 + 23

**Ans**

1. Since, the sum of first *n* odd natural numbers is *n*^{2}.Therefore,1 + 3 + 5 + 7 + 9 = (5)^{2} = 25.

2. Since, the sum of first *n* odd natural numbers is *n*^{2}.Therefore, 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = (10)^{2} = 100.

3. Since, the sum of first *n* odd natural numbers is *n*^{2}.Therefore,1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 +17 + 19 + 21 + 23 = (12)^{2} = 144

**Q.8 **(i) Express 49 as the sum of 7 odd numbers.

(ii) Express 121 as the sum of 11 odd numbers.

**Ans**

(i) We know that the sum of first *n* odd natural numbers is *n*^{2}.Therefore, 49 is the sum of first 7 odd natural numbers.

49 = (7)^{2}

49 = 1 + 3 + 5 + 7 + 9 + 11 + 13

(ii) We know that the sum of first *n* odd natural numbers is *n*^{2}.Therefore, 121 is the sum of first 11 odd natural numbers.

121 = (11)^{2}

121 = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 + 21

**Q.9 **How many numbers lie between squares of the following numbers?

(i) 12 and 13 (ii) 25 and 26 (iii) 99 and 100

**Ans**

We know that there will be 2*n* numbers in between the squares of the numbers *n* and (*n* + 1).

(i) Between 12^{2} and 13^{2}, there will be 2 × 12 = 24 numbers

(ii) Between 25^{2} and 26^{2}, there will be 2 × 25 = 50 numbers

(iii) Between 99^{2} and 100^{2}, there will be 2 × 99 = 198 numbers

## FAQs (Frequently Asked Questions)

### 1. How do students begin their preparation for the Class 8 Mathematics course?

The best resources to start their Class 8 Mathematics preparation are the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. In order to prevent confusion during the exam, they should attempt to cover all the topics in their learning process.

### 2. How can students succeed in CBSE Class 8 Math?

Students can use the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 to perform well on the Class 8 Mathematics Exam. Students should practice as often as they can and thoroughly go over the concepts.

### 3. Where can students find solutions to NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1?

On the Extramarks website, candidates can access the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1.

### 4. Does the Extramarks website offer NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1?

Students can download the PDF versions of NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. These solutions are created specially by efficient instructors of Extramarks. They also offer PDF downloads of the answers to Exercise 6.1 Class 8 Maths.

### 5. How should students study for the Class 8 exams?

Students can take help from the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 to get the best marks in exams.

### 6. In CBSE Class 8, are there any board exams?

The Central Board of Secondary Education administers board exams for only classes 10 and 12. According to CBSE requirements for Class 8, the schools administer the exams.

### 7. Is there a website where students can get the NCERT solutions for Class 8?

On the Extramarks website, students can get the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. The best way to prepare for Class 8 exams is to go through NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1. Once students have finished the syllabus, they can practice with the aid of NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 to attain proficiency in the subject matter.

### 8. What is the most effective way of preparing for Class 8 examinations?

A chapter-by-chapter approach is the most effective way to prepare for the Class 8 annual exams. Once students have completed a chapter, they should review the chapter’s questions. After completing the entire curriculum, students can take the subject-specific practice exams. Students will undoubtedly benefit from this and perform well on their tests.

### 9. Is it possible to get a PDF form of NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1?

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### 10. Are the NCERT Solutions For Class 8 Maths Chapter 6 Exercise 6.1 beneficial to Class 8 students for the preparation for final term exams?

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