Question

Find the smallest natural number by which 1,200 should be multiplied so that the square root of the product is a rational number.

Answer 1

Answer = 3

Factorise 1200 by factor method.
1200=2x2x5x5x2x2x3
So 3 is the smallest natural number by which 1200 should be multiplied so that the square root of the product is a rational number.
1200X 3=3600

The smallest no. is 3
This is because when you prime factorize 1200 you get 2*2*2*2*5*5*3 in which all no. are in pairs except 3
That is if we want to pair nos you will get 2 pair,2 pair, 5 pair but no 3 pair.
So we will multiply it by 3 thus getting 3600 which is the square of 60