NCERT Solutions for Class 8 Mathematics Chapter 6: Square and Square Roots
Mathematics is a subject which requires a deeper understanding of the concepts and problem solving skills . In addition, it also has complex theorems and formulas. Thus, students of class 8 have to prepare with more focus to gain an advantage over the subject. For students interested in this subject, it opens many opportunities in Engineering and Science. Therefore, it is a critical learning stage for them, as it prepares them for the upcoming opportunities in life.
Class 8 Mathematics Chapter 6: Square and Square Roots class 8 is an essential chapter that introduces concepts like finding squares of big numbers by expansion techniques and other patterns observed in square numbers. . It sheds light on square numbers and square roots, their properties, and some exciting patterns.
Extramarks’ NCERT Solutions for Class 8 Mathematics Chapter 6 are available for the students on the website or app of Extramarks. It covers detailed and accurate solutions to questions given in the NCERT textbook, which will help them understand how to solve the different kinds of problems in a step-by- step manner . It consists of 30 questions, of which 21 are medium to hard, four are moderately easy, and 5 are long answer-type questions. Our solution guide revolves around many essential questions that can also appear in the entrance exams.
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For the latest updates and exam-related news, students can visit our Extramarks’ website. Further, they can also refer to other class solutions such as NCERT Solutions Class 10, NCERT Solutions Class 11, and NCERT Solutions Class 12.
Key Topics Covered in NCERT Solutions for Class 8 Mathematics Chapter 6:
The Squares and Square Roots Class 8 – discusses the properties of square numbers. Here, students will learn how to find the sum and product of consecutive even and odd natural numbers and also about Pythagorean triplets. Our NCERT Solutions for Class 8 Mathematics Chapter 6 outline all the formulas for finding square roots with the help of repeated subtraction and through prime factorization and long division method to find the square roots of numbers.
Some of the key topics featured in NCERT Solution for Class 8 Mathematics Chapter 6 are:
Square of a number
If any number is raised to exponent two, it is known as the square of the base. Hence, 25 is referred to as the square of 5, while 64 is the square of 8. One can find the square of a number by multiplying the given number two times. For example, 5 Square = 5 x 5 = 25, whereas 8 Square = 8 x 8 = 64.
If we find the square of a whole number, the resultant number is a perfect square. Numbers such as perfect squares are 4, 9, 16, 25, 36, 49, 64, and so on. Therefore, a square of a number is always a positive number.
To understand the applications of the square of a number, students can refer to NCERT Solutions for Class 8 Mathematics Chapter 6.
Perfect Squares
A perfect square is a number expressed as the product of an integer itself or as the second exponent of an integer. For example, if 25 is a perfect square, it is the product of integer five by itself, 5 x 5 = 25. On the other hand, a number such as 21 is not a perfect square number because it is not eligible to be expressed as the product of two exact integers.
Therefore, a perfect square is a positive integer. It can be obtained by multiplying an integer by itself. In simpler words, one can say that perfect squares are numbers that are the products of integers. Therefore, one can express a perfect square as x2, where x is an integer and 2 is the value of a perfect square.
Properties of Square Numbers
Properties of square numbers explained in NCERT Solutions for Class 8 Mathematics Chapter 6 are:
- Numbers such as 0, 1, 4, 5, 6, or 9 in the unit’s place may or may not be a square.
- Numbers such as 2, 3, 7, or 8 are in their unit place then it is not a square number.
- The number has 1 or 9 in the unit’s place; its square ends in 1.
- If a square number ends in 6, the number will have 4 or 6 in the unit place.
Square Roots
The inverse operation of squaring a number is known as the square root of a number. The value is obtained when we multiply the number by itself.
We can calculate the square root of a number by finding a number that delivers the original number when it is squared. For example, if ‘a’ is the square root of ‘b’, it means that a x a = b. It is said that the square of any number is always a positive number. Hence, every number has two square roots, one of a positive value and one of a negative value.
There are few example elaborated in NCERT Solutions for Class 8 Mathematics Chapter 6:
Numbers such as 2 and -2 are square roots of 4. So in most places, only the positive value is written in the square root of a number.
Square Root of a Negative Number
A square root of a negative number does not give a negative result. The answer is either positive or zero. Besides, complex numbers have a solution to finding a negative number’s square root. The square root of -x is: √(-x)= i√x. Therefore, i is the square root of -1.
For example: If we make a perfect square number like 16. Then, the square root of -16 will not have the real square root of -16. √(-16)= √16 × √(-1) = 4i (as, √(-1)= i), ‘i’ is denoted as the square root of -1.
Finding the square of a number using identity
It is not that difficult to find the square root of a number which is a perfect square. These are the squares whose positive numbers can be expressed as the product of a number itself. In simple words, perfect squares are numbers expressed as any integer’s value of power 2. There are four methods explained in NCERT Solutions for Class 8 Mathematics Chapter 6 are as follows:
- Repeated Subtraction Method of Square Root
- Square Root by Prime Factorization Method
- Square Root by Estimation Method
- Square Root by Long Division Method
The first three methods are usually used for perfect squares, while the fourth method, the long division method, is mainly used for any number, whether it is a perfect square or not. To understand how these different methods are used to find the square of a number, students can refer to NCERT Solutions for Class 8 Mathematics Chapter 6.
Interesting Patterns
There are many exciting patterns observed in square and perfect square roots:
- Adding triangular numbers
- Numbers between square numbers
- Adding odd numbers
- A sum of consecutive natural numbers
- Product of two consecutive even or odd natural numbers
NCERT Solutions for Class 8 Mathematics Chapter 6: Exercise & Solutions
The solutions are prepared by subject experts who have years of experience in teaching. All the answers are stated stepwise for quick retention.
Every answer of every chapter in NCERT Solutions for Class 10 Science is written as per the CBSE guidelines. As the explanations are comprehensive, the fundamentals of the chapter are understood by the students in a better way. The answers in NCERT solutions are explained in detail, which gives students an idea of how to attempt a question in the board exam in the right manner
NCERT Class 8 Mathematics Chapter 6 introduces different techniques used to determine whether a given natural number is a perfect square number or not. These techniques are demonstrated by the properties and patterns followed by square numbers. This chapter also introduces the various methods for finding the square roots of square numbers. Students can click the links below for specific questions and solutions:
Along with this, students can also refer to other solutions for primary and secondary classes:
NCERT Exemplar for Class 8 Mathematics:
Mathematics interests many students, but it is equally challenging as it involves complex problem solving. Many students face difficulty in remembering the concepts and theories. Thus, it is beneficial for them to solve different questions of different a difficulty levels. In addition, it helps students remember the formulas and their use at various stages of problems.
NCERT Exemplar consists of all solved textual questions that are explained in easy to understand language. Going through these questions and answers helps in building a strong foundation on all the concepts. Most of the questions asked in the annual examination are from NCERT books. Further, exemplars offer multiple-choice questions, descriptive-type questions, and objective-type questions.
Key Features of NCERT Solutions for Class 8 Mathematics Chapter 6:
Class 8 Mathematics discusses the properties of square numbers and odd natural numbers. Some of the essential topics such as some interesting patterns, Pythagorean triples, square roots, and square roots of decimals. Our Extramarks NCERT Solutions for Class 8 Mathematics Chapter 6 cover all essential topics and concepts.
The key benefits of NCERT Solutions for Class 8 Mathematics Chapter 6 are listed here:
- The solutions have well-curated examples and solutions to exercise questions covering all the essential concepts of the topic.
- Students can first solve the problems and then cross check their answers from the given solutions.
- Students can solve questions of different difficulty levels, hence fully preparing themselves for the exams.
- By accessing other NCERT study material like important questions from the chapter, frequently asked questions, MCQs, past years’ papers, expert tips & tricks to grasp answers on Extramarks app or website, students can leverage higher marks in their examination.
- The additional questions provided would enable students to practise thoroughly.