Question

Find the smallest number by which 500 must be divided to obtain a perfect cube. Also, find the
cube root of the cubic number thus obtained.

Answer 1

Step-by-step explanation:

A perfect cube should have all of its ‘factors’ occurring in groups of 3.

So, let’s factor 500.

2 * 2 * 5 * 5 * 5

Wow! The only factor that doesn’t occur in a group of 3 is 2. So, we would add one more factor of 2 to get 2 * 2 * 2 * 5 * 5 * 5 = 1000 which happens to be 10 cubed.

So, the answer to your question is 2.

Answer 2

All cube numbers must have factors in groups of 3,

Let us first factorise 500

 

2 | 500               500 = 2 x 2 x 5 x 5 x 5

2 | 250               Here, the number 2 only has a pair and not a triplet

5 | 125                As we are asked in the question to divied 500 to get a

5 |  25                perfect cube, we shall remove the pair of 2s,

5 |    5                2 x 2 = 4  

        1                500/4 = 125

                         125 = 5³