Simplify square root of (y^8)/25

$\sqrt{\frac{y^{8}}{25}}$

Step 1

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

$\sqrt{\frac{{(y^{4})}^{2}}{25}}$

Step 2

Rewrite $25$ as $5^{2}$ .

$\sqrt{\frac{{(y^{4})}^{2}}{5^{2}}}$

Step 3

Rewrite $\frac{{(y^{4})}^{2}}{5^{2}}$ as ${(\frac{y^{4}}{5})}^{2}$ .

$\sqrt{{(\frac{y^{4}}{5})}^{2}}$

Step 4

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

$\frac{y^{4}}{5}$