Question

Find the smallest number by which 200 should be multiplied to make it a perfect cube

Answer 1

2	200
2	100
2	50
5	25
5	5
	1

We find 200 = `bar(2 xx 2 xx 2) xx 5 xx 5`

Grouping the prime factors of 200 as triplets, we are left with 5 × 5

We need one more 5 to make it a perfect cube.

So to make 200 a perfect cube multiply both sides by 5.

200 × 5 = `(bar(2 xx 2 xx 2) xx 5 xx 5) xx 5`

1000 = 2 × 2 × 2 × 5 × 5 × 5 × 5 × 5

Now 1000 is a perfect cube.

∴ The required number is 5.