Simplify square root of (450x^7y^5)/(2x^5y^3)

$\sqrt{\frac{450 x^{7} y^{5}}{2 x^{5} y^{3}}}$

Step 1

Reduce the expression $\frac{450 x^{7} y^{5}}{2 x^{5} y^{3}}$ by cancelling the common factors.

Factor $2$ out of $450 x^{7} y^{5}$ .

$\sqrt{\frac{2 (225 x^{7} y^{5})}{2 x^{5} y^{3}}}$

Factor $2$ out of $2 x^{5} y^{3}$ .

$\sqrt{\frac{2 (225 x^{7} y^{5})}{2 (x^{5} y^{3})}}$

Cancel the common factor.

$\sqrt{\frac{2 (225 x^{7} y^{5})}{2 (x^{5} y^{3})}}$

Rewrite the expression.

$\sqrt{\frac{225 x^{7} y^{5}}{x^{5} y^{3}}}$

Step 2

Cancel the common factor of $x^{7}$ and $x^{5}$ .

Factor $x^{5}$ out of $225 x^{7} y^{5}$ .

$\sqrt{\frac{x^{5} (225 x^{2} y^{5})}{x^{5} y^{3}}}$

Cancel the common factors.

Factor $x^{5}$ out of $x^{5} y^{3}$ .

$\sqrt{\frac{x^{5} (225 x^{2} y^{5})}{x^{5} (y^{3})}}$

Cancel the common factor.

$\sqrt{\frac{x^{5} (225 x^{2} y^{5})}{x^{5} y^{3}}}$

Rewrite the expression.

$\sqrt{\frac{225 x^{2} y^{5}}{y^{3}}}$

Step 3

Cancel the common factor of $y^{5}$ and $y^{3}$ .

Factor $y^{3}$ out of $225 x^{2} y^{5}$ .

$\sqrt{\frac{y^{3} (225 x^{2} y^{2})}{y^{3}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{y^{3} (225 x^{2} y^{2})}{y^{3} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y^{3} (225 x^{2} y^{2})}{y^{3} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{225 x^{2} y^{2}}{1}}$

Divide $225 x^{2} y^{2}$ by $1$ .

$\sqrt{225 x^{2} y^{2}}$

Step 4

Rewrite $225 x^{2} y^{2}$ as ${(15 x y)}^{2}$ .

$\sqrt{{(15 x y)}^{2}}$

Step 5

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

$15 x y$