Question

SQUARES AND SQUARE ROOTS

1. Find the square root of each of the following numbers by using the method of prime

factorization:

1. 225
2. 441
3. 1296
4. 2025

5. 7056
6. 11025
7. 15876
8. 17424​

Answer 1

Solution :-

1) 225

By Prime factorisation,

√225 = √(3² × 5²)

∴ √225 = 3 × 5 = 15

2) 441

By Prime factorisation,

√441 = √(3² × 7²)

∴ √441 = 3 × 7 = 21

3) 1296

By Prime factorisation,

√1296 = √(2⁴ × 3⁴)

∴ √1296 = 2² × 3² = 36

4) 2025

By Prime factorisation,

√2025 = √(3⁴ × 5²)

∴ √2025 = 3² × 5 = 45

5) 7056

By Prime factorisation,

√7056 = √(3² × 4² × 7²)

∴ √7056 = 3 × 4 × 7 = 84

6) 11025

By Prime factorisation,

√11025 = √(3² × 5² × 7²)

∴ √11025 = 3 × 5 × 7 = 105

7) 15876

By Prime factorisation,

√15876 = √(2² × 3⁴ × 7²)

∴ √15876 = 2 × 3² × 7 = 126

8) 17424

By Prime factorisation,

√17424 = √(2⁴ × 3² × 11²)

∴ √17424 = 2² × 3 × 11 = 132