Question

Find the smallest number by which 12748 should be multiplied so that the product is a perfect square. Also find the square root of the resulting number.

Answer 1

on prime factorising 12748 we get that 3187 is not grouped in a pair so 12748 should be multiplied by 3187  to get a perfect sq. no.
the no. will be=40627876
and the root for the same is 2*3187=6374

Answer 2

Given:

Product of 12748 and the smallest number results in a "perfect square".

To find:

"The smallest number"

"Square root" of the resulting number

Answer:    

$12748=2 \times 2 \times 3187$

$\sqrt { 12748 } =\sqrt { 2\times 2\times 3187 } =2\sqrt { 3187 }$

Since 3187 is a "prime number". Hence 12748 should be multiplied with 3187 to get the perfect square

That means

$12748 \times 3187 = 2 \times 2 \times 3187 \times 3187 = 40627876$