How do you simplify $\sqrt[4]{40}$ $root4 (40)$ ?

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How do you simplify $\sqrt[4]{40}$ $root4 (40)$ ?

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Answer 1 · 2017-09-18T16:01:25

$2.514866859$ $2.514866859$

Explanation:

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$\sqrt[4]{40} = 2.514866859$ $root4(40)=2.514866859$

Answer 2 · 2017-09-18T19:04:44

About the most you can do is:

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

Explanation:

The prime factorisation of $40$ $40$ is:

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

Since there are no $4$ $4$ 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:

$\sqrt[4]{40} = \sqrt{\sqrt{2^{2} \cdot 10}} = \sqrt{\sqrt{2^{2}} \cdot \sqrt{10}} = \sqrt{2 \sqrt{10}}$ $root(4)(40) = sqrt(sqrt(2^2*10)) = sqrt(sqrt(2^2)*sqrt(10)) = sqrt(2sqrt(10))$

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