how can we take out cube root of a number and how can we find out that the given number is a perfect cube or not? and plz tell me the method to convert a given number into a perfect cube, like-smallest number to be multiplied with 137592 so that 137592 becomes a perfect cube is-

137592 

It can be prime factorized as:

137592  = 2 × 2 × 2 × 3 × 3 ×1911 ... (1)

Here, only 2 appears in the form of triplet and we know that in order to have a number as a perfect cube it must have all the numbers in triplet.

So, if we multiply (1) by 3 and 1911 × 1911 then we will get

2 × 2 × 2 × 3 × 3 × 1911 × 3 × 1911 × 1911 = 2 × 2 × 2 × 3 × 3 × 3 × 1911 × 1911 × 1911 = 1507425342696

Now, all the number's i.e., 2, 3 and 1911 appears in triplet.

So, 1507425342696 will be the perfect cube of 2 × 3 × 1911 = 11466.