root of the quotient.

       26244

        / \

       2  13122

          / \

         2  6561

            / \

           3  2187

              / \

             3  729

                / \

               3  243

                  / \

                 3  81

                    / \

                   3  27

                      / \

                     3   9

                        / \

                       3   3

So   26244 = 2238  

To become a cube, all the prime factors of it must  

be to a power which is a multiple of 3.

Notice that the prime number base 2 in the factorization

is RAISED to the 2nd power (exponent), but exponent 2 is  

NOT a multiple of 3, so we'll have to multiply by the 1st  

power of 2 so that when we add exponents of 2 we will get 23.

Notice also that the prime number base 3 in the factorization

is raised to the 8TH power (exponent), but exponent 8 is  

NOT a multiple of 3, so we'll have to multiply by the 1st  

power of 3 so that when we add exponents of 3 we will get 39.

So we have to multiply by 2131

or 2∙3 or 6 to cause 26244 to become a perfect cube.

So we have to multiply 2238 by 2131

so that it will become 2339 and both prime bases 2 and 3

will be raised to powers (exponents) which are both MULTIPLES of 3.

So then the cube root of 2339 will be gotten

by dividing each exponent by 3, which will give 2133 which

is 2∙27 or 54.

That's the same as saying

The 26244 must be multiplied by 6 gives 157464 which is a  

perfect cube.  It is a perfect cube because 543 = 157464.

And the cube root is 54 because 54∙54∙54 = 157464.

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