# How do you simplify root4 (40)?

Sep 18, 2017

$2.514866859$

#### Explanation:

By calculator

$\sqrt[4]{40} = 2.514866859$

Sep 18, 2017

About the most you can do is:

$\sqrt[4]{40} = \sqrt{2 \sqrt{10}}$

#### Explanation:

The prime factorisation of $40$ is:

$40 = 2 \cdot 2 \cdot 2 \cdot 5$

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:

$\sqrt[4]{40} = \sqrt{\sqrt{{2}^{2} \cdot 10}} = \sqrt{\sqrt{{2}^{2}} \cdot \sqrt{10}} = \sqrt{2 \sqrt{10}}$