Simplify square root of fifth root of k^11

$\sqrt{\sqrt[5]{k^{11}}}$

Step 1

Rewrite $k^{11}$ as ${(k^{2})}^{5} k$ .

Factor out $k^{10}$ .

$\sqrt{\sqrt[5]{k^{10} k}}$

Rewrite $k^{10}$ as ${(k^{2})}^{5}$ .

$\sqrt{\sqrt[5]{{(k^{2})}^{5} k}}$

$\sqrt{\sqrt[5]{{(k^{2})}^{5} k}}$

Step 2

Pull terms out from under the radical.

$\sqrt{k^{2} \sqrt[5]{k}}$

Step 3

Pull terms out from under the radical.

$k \sqrt{\sqrt[5]{k}}$

Step 4

Rewrite $\sqrt{\sqrt[5]{k}}$ as $\sqrt[10]{k}$ .

$k \sqrt[10]{k}$

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