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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