CBSE Class 8 Maths Chapter 6 Square and Square Roots NCERT Solutions

Reviewed by NCERT Help Editorial Team · Updated on 29 Jul 2026

NCERT Solutions PDF Class 8 PDF

CBSE Class 8 Mathematics Chapter 6, Square and Square Roots, introduces students to the fascinating world of perfect squares and their roots. This chapter explores how to identify the unit digit of the square of any number and understand the key properties that define a perfect square. It also clarifies why certain numbers can never be perfect squares, based on their unit digits and the count of trailing zeros. The NCERT Solutions offer clear, step-by-step explanations to demystify these concepts, ensuring students build a robust understanding. This resource is invaluable for exam preparation and developing a strong foundation in number theory, making revision and practice more effective.

Home

Quick info

Board	CBSE
Class	Class 8
Subject	Mathematics
Session	2026
Language	English
Type	NCERT Solutions
Chapter	Chapter 6: Square and Square Roots

Chapter summary

Chapter 6, 'Square and Square Roots,' for Class 8 Maths NCERT Solutions focuses on understanding the properties of perfect squares. The exercises cover determining the unit digit of squares of given numbers and identifying non-perfect squares based on their unit digits and the count of trailing zeros. This chapter builds foundational number sense crucial for further mathematical concepts.

Learning outcomes

Determine the unit digit of the square of any given number.
Identify the properties of perfect squares related to their unit digits.
Recognize numbers that cannot be perfect squares based on their unit digits.
Understand the rule for trailing zeros in perfect squares.
Apply the properties of squares to justify why a number is not a perfect square.

Topics covered

Paper topics

Unit digit of squares
Properties of perfect squares
Identifying non-perfect squares
Numbers ending in 0, 1, 4, 5, 6, 9
Trailing zeros in perfect squares

Important topics

Unit digit of squares
Properties of perfect squares
Identifying non-perfect squares
Rule for trailing zeros

PDF preview

Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.

Loading document …

Page of

Loading page …

Questions and Solutions

Question 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

Solution:

To find the unit digit of the square of a number, we only need to consider the unit digit of the number itself. Let's find the unit digit of the square for each number:

(i) For 81, the unit digit is 1. The square of 1 is $1^2 = 1$ . So, the unit digit of the square of 81 is 1.

(ii) For 272, the unit digit is 2. The square of 2 is $2^2 = 4$ . So, the unit digit of the square of 272 is 4.

(iii) For 799, the unit digit is 9. The square of 9 is $9^2 = 81$ . So, the unit digit of the square of 799 is 1.

(iv) For 3853, the unit digit is 3. The square of 3 is $3^2 = 9$ . So, the unit digit of the square of 3853 is 9.

(v) For 1234, the unit digit is 4. The square of 4 is $4^2 = 16$ . So, the unit digit of the square of 1234 is 6.

(vi) For 26387, the unit digit is 7. The square of 7 is $7^2 = 49$ . So, the unit digit of the square of 26387 is 9.

(vii) For 52698, the unit digit is 8. The square of 8 is $8^2 = 64$ . So, the unit digit of the square of 52698 is 4.

(viii) For 99880, the unit digit is 0. The square of 0 is $0^2 = 0$ . So, the unit digit of the square of 99880 is 0.

(ix) For 12796, the unit digit is 6. The square of 6 is $6^2 = 36$ . So, the unit digit of the square of 12796 is 6.

(x) For 55555, the unit digit is 5. The square of 5 is $5^2 = 25$ . So, the unit digit of the square of 55555 is 5.

Question 2

The following numbers are obviously not perfect squares. Give reasons.

(i) 1057

(ii) 23453

(iii) 7928

(iv) 222222

(v) 64000

(vi) 89722

(vii) 222000

(viii) 505050

Solution:

A number is not a perfect square if its unit digit is not one of 0, 1, 4, 5, 6, or 9. Additionally, a number ending in zero must have an even number of trailing zeros to be a perfect square.

(i) 1057 is not a perfect square because its unit digit is 7. Perfect squares cannot end in 2, 3, 7, or 8.

(ii) 23453 is not a perfect square because its unit digit is 3. Perfect squares cannot end in 2, 3, 7, or 8.

(iii) 7928 is not a perfect square because its unit digit is 8. Perfect squares cannot end in 2, 3, 7, or 8.

(iv) 222222 is not a perfect square because its unit digit is 2. Perfect squares cannot end in 2, 3, 7, or 8.

(v) 64000 is not a perfect square because it ends with three zeros (an odd number of trailing zeros). Perfect squares ending in zero must have an even count of zeros.

(vi) 89722 is not a perfect square because its unit digit is 2. Perfect squares cannot end in 2, 3, 7, or 8.

(vii) 222000 is not a perfect square because it ends with three zeros (an odd number of trailing zeros). Perfect squares ending in zero must have an even count of zeros.

(viii) 505050 is not a perfect square because it ends with a single zero (an odd number of trailing zeros). Perfect squares ending in zero must have an even count of zeros.

Common mistakes

Incorrectly identifying the unit digit of a square.
Assuming a number ending in 0, 1, 4, 5, 6, or 9 is always a perfect square.
Not considering the number of trailing zeros for numbers ending in 0.
Confusing the unit digit of a number with the unit digit of its square.

Revision tips

Memorize the unit digits of squares for numbers 0 through 9.
Practice identifying the unit digit of squares without full calculation.
Focus on the rules for unit digits and trailing zeros to quickly identify non-perfect squares.
Review the reasons provided for why numbers are not perfect squares.

Practice MCQs

Q1. What is the unit digit of the square of 799?

Q2. Which of the following numbers cannot be a perfect square because its unit digit is 7?

Q3. What is the unit digit of the square of 26387?

Q4. Why is 64000 not a perfect square?

Q5. The unit digit of the square of 55555 will be:

Q6. Which of these numbers is not a perfect square?

Frequently asked questions

What is the main focus of Chapter 6: Square and Square Roots for Class 8 Maths?

This chapter focuses on understanding the properties of square numbers, particularly how to determine the unit digit of the square of any number and how to identify numbers that are not perfect squares based on their unit digits and the number of trailing zeros.

How can I find the unit digit of the square of a large number like 26387?

To find the unit digit of the square of a large number, you only need to consider the unit digit of the original number. For 26387, the unit digit is 7. The square of 7 is 49. Therefore, the unit digit of the square of 26387 is 9.

What are the possible unit digits of perfect squares?

The possible unit digits of perfect squares are 0, 1, 4, 5, 6, and 9.

Why are numbers like 1057 or 7928 not perfect squares?

Numbers like 1057 and 7928 are not perfect squares because their unit digits are 7 and 8, respectively. Perfect squares cannot end in 2, 3, 7, or 8.

What is the rule regarding zeros for a number to be a perfect square?

A number ending in zero can only be a perfect square if it has an even number of trailing zeros. For example, 400 (two zeros) is a perfect square (20²), but 4000 (three zeros) is not.

How do these NCERT Solutions help in exam preparation?

These solutions provide clear, step-by-step explanations for each problem, helping you understand the underlying concepts and methods. They reinforce the rules and properties of squares and square roots, enabling you to solve similar problems confidently during exams.

Content reviewed by the NCERT Help team. Editorial Team and update policy

NCERT Solutions PDF PDF on NCERT Help. URL unchanged for search indexing.