Question

find the least number by which 7688 should be multiplied so that the resulting number become a perfect square

Answer 1

Hello friend!!

Here's your answer.

Prime factorisation of 7688 is 
2 × 2 × 2 × 31 × 31
= 2^3 × 31^2

A number is a perfect square if it's factors have even exponential powers 

But here 2 has an odd exponential power

So if we multiply 2 to 7688 it will have even exponential power of both 2 and 31.

Therefore, 2 is the smallest number that must be multiplied to make 7688 a perfect square

HOPE THAT HELPS..... :-)☺️