Question

How do you simplify `(-5+5root4(5))/(3root4(6))`?

Answer 1

`(5(root(4)(5) -1))/(3 root(4)(6)) = 5/18(root(4)(5)-1)6^(3/4)`

Explanation:

Given: `(-5 + 5root(4)(5))/(3 root(4)(6))`

To simplify factor a `5` in the numerator: `(5(root(4)(5) -1))/(3 root(4)(6))`

This could be considered a simplified solution, although it is possible to eliminate the denominator knowing that `root(4)(6) = 6^(1/4)`. Multiply both numerator and denominator by `6^(3/4)`:

`(5(root(4)(5) -1))/(3 * 6^(1/4)) * (6^(3/4))/(6^(3/4)) = (5(root(4)(5) -1)6^(3/4))/(3 * 6^(1/4) * 6^(3/4)) = (5(root(4)(5) -1)6^(3/4))/(3 * 6)`

`= 5/18(root(4)(5)-1)6^(3/4)`