Simplify fourth root of y^10

$\sqrt[4]{y^{10}}$

Step 1

Rewrite $y^{10}$ as ${(y^{2})}^{4} y^{2}$ .

Factor out $y^{8}$ .

$\sqrt[4]{y^{8} y^{2}}$

Rewrite $y^{8}$ as ${(y^{2})}^{4}$ .

$\sqrt[4]{{(y^{2})}^{4} y^{2}}$

Step 2

Pull terms out from under the radical.

$y^{2} \sqrt[4]{y^{2}}$

Step 3

Rewrite $\sqrt[4]{y^{2}}$ as $\sqrt{\sqrt{y^{2}}}$ .

$y^{2} \sqrt{\sqrt{y^{2}}}$

Step 4

Pull terms out from under the radical, assuming positive real numbers.

$y^{2} \sqrt{y}$