How do you simplify $root4 (40)$ ?

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Answer 1 · 2017-09-18T16:01:25

$2.514866859$

By calculator

$root4(40)=2.514866859$

Answer 2 · 2017-09-18T19:04:44

About the most you can do is:

$root(4)(40) = sqrt(2sqrt(10))$

The prime factorisation of $40$ is:

$40 = 2*2*2*5$

Since there are no $4$ th powers, it is not possible to "move a factor" outside the radical.

It is possible to move one factor "half way" out, since we do have a square factor.

So we find:

$root(4)(40) = sqrt(sqrt(2^2*10)) = sqrt(sqrt(2^2)*sqrt(10)) = sqrt(2sqrt(10))$

How do you simplify root4 (40)root4 (40)?