Question

How do you simplify `(root4(5))/(4root4(27))`?

Answer 1

`(root(4)15)/12`

Explanation:

`(root(4)5)/(4*root(4)27)`, we first want to remove the radicals from the denominator, we can do this by multiplying by `root(3/4)27/root(3/4)27` which is equal to `1`.

`(root(4)5)/(4*root(4)27) * root(4)27^3/root(4)(27)^3 = (root(4)5*root(4)27^3)/(4*root(4)27*root(4)27^3) = (root(4)5*root(4)27^3)/(4*root(4)27^4) = (root(4)5*root(4)27^3)/(4*27)`

`=(root(4)5*root(4)27*root(4)27*root(4)27)/108 = (root(4)(5*27^3))/108 =(root(4)(5*3^9))/108 = (root(4)(5*3^4 * 3^4 * 3))/108 =(3*3root(4)(5*3))/108 = (9root(4)(15))/(9*12) = (cancel9root(4)(15))/(cancel9*12)`

This is as simplified as it gets,

`(root(4)15)/12`