Question

Find the number by which 5400 must be multiplied so that the product is a perfect cube.

Also find the cube root of the number obtained.

( Show workings )​

Answer 1

Explanation:

The easiest way (or the most reliable way) is to factor the given number into primes

5400 = 2 * 2 * 2 * 3 * 3 * 3 * 5 * 5

I cheated a little bit. 54 = 2 * 27 which is 2 * 3 * 3 * 3

100 = 2 * 2 * 5 *5

Combine the two parts and you get the factors I gave you.

Now you have to have the numbers go into groups of three. The only adjustment needed is 5 * 5 and one more 5

So the perfect cube is 5400 * 5 = 27000

Does that work? It should

27000^(1/3) = 3 * 10 = 30

So the cube root of 27000 is 30.