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

847 = 7 × 11 × 11

Here we observe that 7 appears only once. 

∴The required number of multiplied is 7.

(ii) 450

450 = 2 × 5 × 5 × 3 × 3 

Here we observe that 2 appears only once 

∴ The required number is 2.

(iii) 1445

1445 = 5 × 17 × 17 

Here we observe that 5 appears only once 

∴ The required number of multiplied is 5.

(iv) 1352

1352 = 2 × 2 × 2 × 13 × 13 

= 2 × 13 × 2 × 13 × 2 

= 26 × 26 × 2 

Here we observe that 2 appears only once in the product.

∴ The required number multiplier is 2