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

2 Answers
José F.
Apr 15, 2016

#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)#

Tony B
Apr 15, 2016

#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)#

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