Question

Find the smallest natural number by which 60 must be multiplied to obtain a perfect cube.

Answer 1

Answer:

Given no. is 60

Let us try to find at least 2 nos a and b such that:

a x b = 60

at least one of them is a perfect square

60 = 30 x 2 ; 60 = 20 x 3 ; 60 = 12 x 5; 60 = 10 x 6

In the above cases, Neither a nor b is a perfect square.

The next possibility is,

60 = 15 x 4

4 is already a perfect square. No treatment required => 4 x 1 = 4

15 is not a square: It should be multiplied with 15 to make a perfect square => 15 x 1 5 = 225

Final number = 60 x (1 x 15) = 900, which is a perfect square.

Ans: 15 is the smallest number by which 60 must be multiplied to be a perfect square.