Question

How do you rationalize the denominator and simplify `2/root4(2)`?

Answer 1

`root(4)(2^3)`

Explanation:

We have to multiply both sides of the division by `sqrt(2^3)`:

`2/root(4)(2)xxroot(4)(2^3)/root(4)(2^3)=(2root(4)(2^3))/root(4)(2xx2^3)`

`=(2root(4)(2^3))/root(4)(2^4)=(2root(4)(2^3))/2=root(4)(2^3)`

Answer 2

`root(4)(8)`

Explanation:

Given:`" "2/root(4)(2)`

'~~~~~~~~~~~~~~~~~~~~~~~~~
If you have `3sqrt(2)` you may take the 3 inside the squar root as long as you square. So `3sqrt(2)-=sqrt(3^2xx2)`. In the same way if we had `3root(4)(2) -= root(4)(3^4xx2)" "` The three dashes instead of = means equivalent to.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~

Applying this idea we have

`root(4)(2^4/2) = root(4)(2^3) = root(4)(8)`