Question

Find the smallest positive integer with which one has to multiply to get perfect square- 450

Answer 1

450.

So begin by prime factoring 60:

2 X 30 => 2 X 2 X 15 => 2 x 2 X 3 X 5.

To be a perfect cube there should be a multiple of 3 for each prime factor.

2: you have two 2s, if you had three 2s it would be a perfect cube for 2. So you need one more 2.

3: you have one 3, if you had three 3s it would be a perfect cube for 3. So you need two more 3s.

5: you have one 5, if you had three 5s it would be perfect cube for 5. So you need two more 5s.

2 X 3 X 3 X 5 x 5 = 450.

Check 450 X 60 =27000. Cube root of 27000 = 30.