CBSE Class 8 Maths Chapter 6: Squares and Square Roots NCERT Solutions
CBSE Class 8 Mathematics Chapter 6, Squares and Square Roots, introduces fundamental concepts essential for number theory. This chapter delves into identifying the unit digit of a number's square and understanding the characteristics of perfect squares. Students will learn to determine why certain numbers, based on their unit digits or the count of trailing zeros, cannot be perfect squares. Mastering these principles is vital for developing a robust understanding of arithmetic operations and problem-solving. The NCERT Solutions provide clear, step-by-step explanations, enabling students to grasp the underlying logic, practice various problem-solving techniques, and prepare thoroughly for their examinations. This chapter lays a crucial groundwork for future mathematical studies.
Quick info
| Board | CBSE |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Session | 2026 |
| Language | English |
| Type | NCERT Solutions |
| Chapter | Chapter 6 |
Chapter summary
Chapter 6 of the CBSE Class 8 Mathematics syllabus deals with Squares and Square Roots. This NCERT Solutions set offers detailed explanations for exercises related to identifying the unit digit of squares of numbers and understanding the properties of perfect squares. It clarifies why numbers ending in certain digits or having an odd number of trailing zeros cannot be perfect squares. The solutions provide a clear understanding of these fundamental concepts, aiding students in their practice and revision.
Learning outcomes
- Understand the concept of squaring a number.
- Determine the unit digit of the square of any given number.
- Identify the unit digits that perfect squares can end with.
- Recognize properties of perfect squares related to their unit digits.
- Explain why a number is not a perfect square based on its unit digit.
- Understand the rule regarding the number of trailing zeros in perfect squares.
Topics covered
Paper topics
- Squares of numbers
- Unit digit of squares
- Properties of perfect squares
- Unit digits of perfect squares
- Trailing zeros in perfect squares
- Identifying non-perfect squares
Important topics
- Unit digit of squares
- Properties of perfect squares
- Identifying non-perfect squares based on unit digits
- Identifying non-perfect squares based on trailing zeros
PDF preview
Read page by page below. PDF is streamed from the official NCERT website — no download button on this page.
Questions and Solutions
Exercise 6.1, Question 1
(i) 81
(ii) 272
(iii) 799
(iv) 3853
(v) 1234
(vi) 26387
(vii) 52698
(viii) 99880
(ix) 12796
(x) 55555
To find the unit digit of the square of a number, we only need to consider the unit digit of the original number. We square this unit digit and look at its unit digit.
(i) The unit digit of 81 is 1. The square of 1 is $1^2 = 1$. Therefore, the unit digit of the square of 81 is 1.
(ii) The unit digit of 272 is 2. The square of 2 is $2^2 = 4$. Therefore, the unit digit of the square of 272 is 4.
(iii) The unit digit of 799 is 9. The square of 9 is $9^2 = 81$. The unit digit of 81 is 1. Therefore, the unit digit of the square of 799 is 1.
(iv) The unit digit of 3853 is 3. The square of 3 is $3^2 = 9$. Therefore, the unit digit of the square of 3853 is 9.
(v) The unit digit of 1234 is 4. The square of 4 is $4^2 = 16$. The unit digit of 16 is 6. Therefore, the unit digit of the square of 1234 is 6.
(vi) The unit digit of 26387 is 7. The square of 7 is $7^2 = 49$. The unit digit of 49 is 9. Therefore, the unit digit of the square of 26387 is 9.
(vii) The unit digit of 52698 is 8. The square of 8 is $8^2 = 64$. The unit digit of 64 is 4. Therefore, the unit digit of the square of 52698 is 4.
(viii) The unit digit of 99880 is 0. The square of 0 is $0^2 = 0$. Therefore, the unit digit of the square of 99880 is 0.
(ix) The unit digit of 12796 is 6. The square of 6 is $6^2 = 36$. The unit digit of 36 is 6. Therefore, the unit digit of the square of 12796 is 6.
(x) The unit digit of 55555 is 5. The square of 5 is $5^2 = 25$. The unit digit of 25 is 5. Therefore, the unit digit of the square of 55555 is 5.
Exercise 6.1, Question 2
(i) 1057
(ii) 23453
(iii) 7928
(iv) 222222
(v) 64000
(vi) 89722
(vii) 222000
(viii) 505050
A number is not a perfect square if its unit digit is one of 2, 3, 7, or 8. Also, a number ending in an odd number of zeros cannot be a perfect square.
(i) 1057 is not a perfect square because its unit digit is 7.
(ii) 23453 is not a perfect square because its unit digit is 3.
(iii) 7928 is not a perfect square because its unit digit is 8.
(iv) 222222 is not a perfect square because its unit digit is 2.
(v) 64000 is not a perfect square because it ends with three (an odd number) zeros.
(vi) 89722 is not a perfect square because its unit digit is 2.
(vii) 222000 is not a perfect square because it ends with three (an odd number) zeros.
(viii) 505050 is not a perfect square because it ends with a single zero (an odd number of zeros).
Common mistakes
- Incorrectly identifying the unit digit of a number's square.
- Assuming a number is a perfect square without checking its unit digit.
- Misunderstanding the rule for trailing zeros in perfect squares.
- Confusing properties of squares with properties of square roots.
Revision tips
- Memorize the unit digits of squares from 0 to 9.
- Practice identifying the unit digit of squares for large numbers quickly.
- Focus on the properties of perfect squares, especially regarding unit digits and zeros.
- Use the provided reasons to quickly eliminate non-perfect squares.
Practice MCQs
Q1. What is the unit digit of the square of 799?
Explanation: The unit digit of 799 is 9. The square of 9 is 81, so the unit digit of the square of 799 is 1.
Q2. Which of the following unit digits cannot be the unit digit of a perfect square?
Explanation: Perfect squares can only end in 0, 1, 4, 5, 6, or 9. A unit digit of 3 indicates the number is not a perfect square.
Q3. Why is 64000 not a perfect square?
Explanation: A perfect square cannot end with an odd number of zeros. 64000 has three trailing zeros, which is an odd number.
Q4. What is the unit digit of the square of 272?
Explanation: The unit digit of 272 is 2. The square of 2 is 4, so the unit digit of the square of 272 is 4.
Q5. Which of the following numbers is not a perfect square because its unit digit is 7?
Explanation: Perfect squares cannot end in 7. Therefore, 1057 is not a perfect square.
Frequently asked questions
What is the main focus of CBSE Class 8 Maths Chapter 6 NCERT Solutions?
These solutions focus on understanding squares of numbers, determining the unit digit of squares, and learning the properties of perfect squares, including why certain numbers cannot be perfect squares.
How do these solutions help in finding the unit digit of a square?
The solutions explain that the unit digit of a square depends only on the unit digit of the original number. By squaring the unit digit of the number, you can find the unit digit of its square.
What are the key properties of perfect squares discussed in this chapter?
The chapter highlights that perfect squares can only end in digits 0, 1, 4, 5, 6, or 9. Additionally, perfect squares must have an even number of trailing zeros.
Can a number ending in 0 be a perfect square?
Yes, but only if it has an even number of trailing zeros. For example, 100 (two zeros) is a perfect square (10²), but 10 (one zero) is not.
How can I use these NCERT solutions for exam revision?
Review the step-by-step solutions to reinforce your understanding of the concepts. Practice identifying unit digits and applying the properties of perfect squares to solve problems quickly and accurately.
Are there any specific numbers that are guaranteed not to be perfect squares?
Yes, numbers ending in 2, 3, 7, or 8 are never perfect squares. Also, numbers ending in an odd number of zeros are not perfect squares.
Content reviewed by the NCERT Help team. Editorial Team and update policy
NCERT Solutions PDF PDF on NCERT Help. URL unchanged for search indexing.