Question

Find the smallest positive integer with which one has to multiply each of the following numbers to get a perfect square:

(i) 847; (ii) 450; (iii) 1445; (iv) 1352.

Answer 1

(i) 847 = 7 × 11 × 11

847 × 7 = 7 × 7 × 11 × 11

Hence, the required integer is 7.

(ii) 450 = 2 × 3 × 3 × 5 × 5

450 × 2 = 2 × 2 × 3 × 3 × 5 × 5

Hence, the required integer is 2.

(iii) 1445 = 5 × 17 × 17

1445 × 5 = 5 × 5 × 17 × 17

Hence, the required integer is 5.

(iv) 1352 = 2 × 2 × 2 × 13 × 13

1352 × 2 = 2 × 2 × 2 × 2 × 13 × 13

Hence, the required integer is 2.