NCERT Solutions for Class 8 Maths Chapter 5 Square and Square Roots - PDF Download

NCERT solutions for class 8 maths chapter 5 Square and Square Roots provides information on square numbers, square roots, properties of squares and some interesting relationships between them. NCERT solutions for class 8 maths chapter 5 also covers concepts such as finding squares of large numbers by expansion methods and other patterns seen in square numbers. 

In this chapter you will learn about the different methods used to find out if a natural number is a perfect square or not. These methods are shown by properties and patterns that follow by square numbers. This chapter also discusses the different ways to find the square roots of a square number. 

NCERT solution for class 8 maths chapter 5 Square and Square Roots is very helpful for the students as it helps them to score high marks on the exam. eSaral’s mathematics expert team has explained the concepts in a simple and precise way. The solution uses different shortcut hints as well as practical examples to make the exercise questions easy to understand. The pdf format of chapter 5 of NCERT solutions for class 8 maths can be downloaded free of cost from the official website of eSaral. NCERT solutions for class 8 maths chapter 5 pdf must be solved by students in order to achieve a high score in the examination.

Important Topics covered in Chapter 5 - Square and Square Roots

NCERT solutions for class 8 maths Chapter 5 Square and Square Roots, is an essential chapter. It is also the fundamental chapter of maths for higher classes. Consequently, students must be well-versed in the concepts of Square and Square Roots prior to progressing to solving questions.

We have provided an overview of the topics of NCERT solutions for class 8 maths chapter 5 to assist students in comprehending the concepts of the chapter.

5.1 Introduction - The area of a square = side × side (where ‘side’ means ‘the length of a side’). 

Since, 4 can be expressed as 2 × 2 = 2² , 9 can be expressed as 3 × 3 = 3², all such numbers can be expressed as the product of the number with itself. Such numbers like 1, 4, 9, 16, 25, ... are known as square numbers. 

In general, if a natural number m can be expressed as n 2 , where n is also a natural number, then m is a square number.

5.2 Properties of Square Numbers -  The properties of squares as explained in NCERT solution for class 8 maths chapter 5 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. 

5.3 Some more Interesting Patterns - There are some interesting patterns to find the square and 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.

• Some more patterns in square numbers.

5.4 Finding the square of a Number - Squares of small numbers like 3, 4, 5, 6, 7, ... etc. are easy to find. But finding squares of two digit numbers can be difficult. There is a way to find this without having to multiply the numbers.

           5.4.1 Other patterns in squares

           5.4.2 Pythagorean triplets 

5.5 Square Roots - The inverse operation of squaring a number is known as the square root of a number. The square root of the number is the value obtained when multiplying the number by itself.

Finding the number with the known square is known as finding the square root. There are many methods to find the square roots in this section.

           5.5.1 Finding square roots

           5.5.2 Finding square root through repeated subtraction

           5.5.3 Finding square root through prime factorisation

           5.5.4 Finding square root by division method

5.6 Square Roots of Decimals - The number of times a decimal number is raised to the power of 1/2 is referred to as the square root of that decimal number. For example, the number 24.01 is calculated as 4.9 x (4.9 + 1 / 2) = 24.01

You can use either the estimation approach or long division method to figure out the square roots of decimals.

NCERT Solutions for Class 8 Maths Chapter 5 Exercises

To gain a better and quicker comprehension of the concepts, an exercise-based analysis of NCERT solution for class 8 maths chapter 5 Squares & Square Roots is provided in the pdf below.

Benefits of Downloading The NCERT Solutions for Class 8 Maths Chapter 5 - Square and Square Roots

Chapter 5 Squares and Square Roots of class 8 maths book deals with square and square roots. Downloading NCERT solutions for this chapter can bring many benefits to students.

1. The NCERT solutions by eSaral contain well-structured examples and exercise questions with answers that cover all the fundamental concepts of the topic.

2. Free PDF format of NCERT solutions for class 8 mathematics chapter 5 can be downloaded from the eSaral website. You can download the pdf and practice at your convenience. You can carry pdf anywhere and at any time.

3. The answers to each question have been provided by our subject experts in a straightforward and sequential way so that it is easy to understand.

4. These NCERT solutions will not only increase your self-confidence but will also help you in managing your time during the exams. In case you have any doubts about the topics, then you can totally trust the NCERT solutions provided by our expert teachers at eSaral.

Frequently Asked Questions

Question 1. What are square numbers in NCERT solutions for class 8 maths chapter 5 ?

Answer 1. ‘a’ can be considered a square number if any natural number, for example, "a" can be expressed as "n2", where "n" is a natural number. At the unit position, every square number ends with zero, one, four, five, six, or nine. You can only find a square number with an even number at the end. The square root is the inverse operation of the square. A perfect square number contains two integral square roots.

Question 2. How can students make better use of NCERT solutions for class 8 maths chapter 5 ?

Answer 2. NCERT solutions provide well-structured solved examples and exercise questions that cover the fundamental concepts of chapter 5. So, it's important for students to read the chapter clearly first to get a good grasp of it. You should also pay attention to the highlights between chapters. You should complete the exercises and cross-reference their answers from these solutions.