Question

What is the smallest positive integer that can be multiplied times 18 to make a perfect cube?

Answer 1

Answer:

12

Step-by-step explanation:

To solve this, we need to apply the rule that (a × b)ⁿ = aⁿ ×  bⁿ

In other words, if we multiply two numbers that are raised to same power, we will get the same value as their product raised to that power.

In the case of 18, if we break it down to primary factors, we get:

3 × 3 × 2

= 3² × 2

To get a perfect cube, we need each of those factors to  become a perfect cube as well.  To do that we simply multiply by:

3 × 2² (which equals 12)

giving us:

3² × 2 × 3 × 2²

= 3³ × 2³

If we solve that we get:

= 27 × 8

= 216

which is the cube of 2 × 3, or 6³.

So the number you had to multiply by was 12.