NCERT Class 8 Mathematics Mathematics: Chapter 5 — Squares and Square Roots
Chapter 5 of the NCERT Class 8 Mathematics textbook introduces the concept of squares and square roots. It defines a square number as a natural number that can be expressed as the product of a number with itself (m = n^2). The chapter provides examples of square numbers like 1, 4, 9, 25, and 64, and explains how to identify them. It also discusses the properties of square numbers, particularly the digits that appear in the units place of perfect squares (0, 1, 4, 5, 6, 9). The chapter encourages students to explore these properties further and apply them to determine if a given number is a perfect square. This foundational understanding is crucial for further mathematical concepts in CBSE.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 8 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 5 — Squares and Square Roots |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 3 minutes |
| Word count | 436 |
Learning outcomes
- Define and identify square numbers (perfect squares).
- Understand the relationship between a number and its square.
- Recognize the pattern of the unit digits of square numbers.
- Determine if a number is a perfect square based on its unit digit.
- Apply the concept of squares to calculate areas of squares.
Vocabulary
| Word | Meaning |
|---|---|
| Square number | A number that can be expressed as the product of a natural number with itself (e.g., 9 = 3 × 3). |
| Perfect square | Another term for a square number. |
| Natural number | Positive integers starting from 1 (1, 2, 3,...). |
| Unit digit | The digit in the ones place of a number. |
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Practice questions
- What is the square of 7? Answer: 49
- Is 32 a square number? Explain why or why not. Answer: No, because there is no natural number between 5 and 6 whose square is 32. 5^2 = 25 and 6^2 = 36.
- List the square numbers between 50 and 60. Answer: There are no perfect square numbers between 50 and 60. (7^2 = 49, 8^2 = 64).
- Which digits can be the unit digit of a square number? Answer: 0, 1, 4, 5, 6, or 9.
Frequently asked questions
What is a square number in mathematics?
A square number is a natural number that can be obtained by multiplying a natural number by itself. For example, 9 is a square number because 3 × 3 = 9.
What are the possible unit digits of a square number?
The unit digits of square numbers can only be 0, 1, 4, 5, 6, or 9.
Can a number ending in 2, 3, 7, or 8 be a perfect square?
No, a number ending in 2, 3, 7, or 8 cannot be a perfect square.
How do you find the area of a square?
The area of a square is calculated by multiplying the length of its side by itself (side × side).
Is 100 a square number?
Yes, 100 is a square number because 10 × 10 = 100.
How can you tell if 23453 is a perfect square?
Since 23453 ends in 3, it cannot be a perfect square.
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NCERT Class 8 Mathematics — Mathematics — Chapter 5 — Squares and Square Roots. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.