Simplify square root of cube root of 5y^6

$\sqrt{\sqrt[3]{5 y^{6}}}$

Rewrite $5 y^{6}$ as ${(y^{2})}^{3} \cdot 5$ .

Rewrite $y^{6}$ as ${(y^{2})}^{3}$ .

$\sqrt{\sqrt[3]{5 {(y^{2})}^{3}}}$

Reorder $5$ and ${(y^{2})}^{3}$ .

$\sqrt{\sqrt[3]{{(y^{2})}^{3} \cdot 5}}$

$\sqrt{\sqrt[3]{{(y^{2})}^{3} \cdot 5}}$

Pull terms out from under the radical.

$\sqrt{y^{2} \sqrt[3]{5}}$

Pull terms out from under the radical.

$y \sqrt{\sqrt[3]{5}}$

Rewrite $\sqrt{\sqrt[3]{5}}$ as $\sqrt[6]{5}$ .

$y \sqrt[6]{5}$

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