Question

find the smallest number by which 23232 should be divided so that the quotient is a perfect square also find the square root of the new number

Answer 1

prime factors of 23232 = 2*2*2*2*2*2*3*11*11

so,3 is the no. without pair
so, 3 is the no. through which 23232 must be divided to make the quotient a perfect square

23232/3 = 7744

and the square root of 7744 = 88 ans

Answer 2

firstly we have to find the prime factors of 23232
23232 = 2*2*2*2*2*2*3*11*11
while grouping we observe that the prime factor 3 does not form a pair .
so, we divide 23232 by 3 to make it a perfect square
new number = 23232/3 = 7744
√7744 = √2*2*2*2*2*2*11*11
           = 2*2*2*11
√7744 = 88