Question

Find the smallest natural number by which 1200 should be multiplied so that the square root of the product is a rational number

Answer 1

The smallest no. is 3
this is bcuz when u prime factorize 1200 u 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 u will get 2 pair of 2(2x2x2x2), 1pair of 5(5x5) but no 3 pair. so we will multiply it by 3 thus getting 3600 which is the square of 60