Question

Now compute the square root of these by factorization.

(i) 3025

(ii) 2304

(iii) 9604

(iv) 6561

Answer 1

(i) 3025 = 5 × 5 × 11 × 11

= 5² × 11²

= (5 × 11)²

= 55²

We know that for two numbers x and y, if x² = y, then.

So,

(ii) 2304 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3

= 2⁸ × 3²

= (2⁴)² × 3² [since x²ⁿ = (xⁿ)²]

= 16² × 3²

= (16 × 3)²

= 48²

We know that for two numbers x and y, if x² = y, then.

So,

(iii) 9604 = 2 × 2 × 7 × 7 × 7 × 7

= 2² × 7⁴

= 2² × (7²)² [since x²ⁿ = (xⁿ)²]

= 2² × (49)²

= (2 × 49)²

= 98²

We know that for two numbers x and y, if x² = y, then.

So,

(iv) 6561 = 3 × 3 × 3 × 3 × 3 × 3 × 3 × 3

= 3⁸

= (3⁴)² [since x²ⁿ = (xⁿ)²]

= 81²

We know that for two numbers x and y, if x² = y, then.

So,