Simplify square root of (x^6)/(9y^2)

$\sqrt{\frac{x^{6}}{9 y^{2}}}$

Step 1

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

$\sqrt{\frac{{(x^{3})}^{2}}{9 y^{2}}}$

Step 2

Rewrite $9 y^{2}$ as ${(3 y)}^{2}$ .

$\sqrt{\frac{{(x^{3})}^{2}}{{(3 y)}^{2}}}$

Step 3

Rewrite $\frac{{(x^{3})}^{2}}{{(3 y)}^{2}}$ as ${(\frac{x^{3}}{3 y})}^{2}$ .

$\sqrt{{(\frac{x^{3}}{3 y})}^{2}}$

Step 4

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

$\frac{x^{3}}{3 y}$