Simplify square root of (80x^9y^6)/(5xy^2)

$\sqrt{\frac{80 x^{9} y^{6}}{5 x y^{2}}}$

Step 1

Reduce the expression $\frac{80 x^{9} y^{6}}{5 x y^{2}}$ by cancelling the common factors.

Factor $5$ out of $80 x^{9} y^{6}$ .

$\sqrt{\frac{5 (16 x^{9} y^{6})}{5 x y^{2}}}$

Factor $5$ out of $5 x y^{2}$ .

$\sqrt{\frac{5 (16 x^{9} y^{6})}{5 (x y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{5 (16 x^{9} y^{6})}{5 (x y^{2})}}$

Rewrite the expression.

$\sqrt{\frac{16 x^{9} y^{6}}{x y^{2}}}$

Step 2

Cancel the common factor of $x^{9}$ and $x$ .

Factor $x$ out of $16 x^{9} y^{6}$ .

$\sqrt{\frac{x (16 x^{8} y^{6})}{x y^{2}}}$

Cancel the common factors.

Factor $x$ out of $x y^{2}$ .

$\sqrt{\frac{x (16 x^{8} y^{6})}{x (y^{2})}}$

Cancel the common factor.

$\sqrt{\frac{x (16 x^{8} y^{6})}{x y^{2}}}$

Rewrite the expression.

$\sqrt{\frac{16 x^{8} y^{6}}{y^{2}}}$

Step 3

Cancel the common factor of $y^{6}$ and $y^{2}$ .

Factor $y^{2}$ out of $16 x^{8} y^{6}$ .

$\sqrt{\frac{y^{2} (16 x^{8} y^{4})}{y^{2}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{y^{2} (16 x^{8} y^{4})}{y^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y^{2} (16 x^{8} y^{4})}{y^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{16 x^{8} y^{4}}{1}}$

Divide $16 x^{8} y^{4}$ by $1$ .

$\sqrt{16 x^{8} y^{4}}$

Step 4

Rewrite $16 x^{8} y^{4}$ as ${(4 x^{4} y^{2})}^{2}$ .

$\sqrt{{(4 x^{4} y^{2})}^{2}}$

Step 5

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

$4 x^{4} y^{2}$