Chapter 3 · ICSE Class 8 Mathematics

Squares and Square Roots

Learn to recognize perfect squares, and find square roots using prime factorization and estimation.

√ Chapter 3

A 4 by 4 grid showing that 4 squared equals 16 A grid of 16 small unit squares arranged 4 by 4, illustrating that 4 times 4 (4 squared) equals 16 4 × 4 = 16 4² = 16, so √16 = 4
3.1

Perfect Squares

A perfect square is a number that results from multiplying a whole number by itself. Recognizing perfect squares helps quickly identify whether a number has a whole-number square root.

1

Is 49 a perfect square?

Yes, since 7 × 7 = 49

2

Is 50 a perfect square?

No, since no whole number multiplied by itself gives 50

3.2

Finding Square Roots by Prime Factorization

To find the square root of a perfect square, break it into prime factors, then pair up identical factors — each pair contributes one factor to the square root.

1

Find the square root of 144 using prime factorization.

144 = 2×2×2×2×3×3 = (2×2)×(2×2)×(3×3); pairing gives √144 = 2×2×3 = 12

2

Find the square root of 225 using prime factorization.

225 = 3×3×5×5; pairing gives √225 = 3×5 = 15

Practice

Exercises

1. Is 64 a perfect square? If so, what is its square root?

2. Is 90 a perfect square?

3. Find the square root of 196 using prime factorization.

4. Find the square root of 324 using prime factorization.

5. Find the square root of 400 using prime factorization.

Next chapter — Chapter 4: Cubes and Cube-Roots 🧊 →