Simplify square root of (63x^15y^9)/(7xy^11)

$\sqrt{\frac{63 x^{15} y^{9}}{7 x y^{11}}}$

Step 1

Reduce the expression $\frac{63 x^{15} y^{9}}{7 x y^{11}}$ by cancelling the common factors.

Factor $7$ out of $63 x^{15} y^{9}$ .

$\sqrt{\frac{7 (9 x^{15} y^{9})}{7 x y^{11}}}$

Factor $7$ out of $7 x y^{11}$ .

$\sqrt{\frac{7 (9 x^{15} y^{9})}{7 (x y^{11})}}$

Cancel the common factor.

$\sqrt{\frac{7 (9 x^{15} y^{9})}{7 (x y^{11})}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{15} y^{9}}{x y^{11}}}$

Step 2

Cancel the common factor of $x^{15}$ and $x$ .

Factor $x$ out of $9 x^{15} y^{9}$ .

$\sqrt{\frac{x (9 x^{14} y^{9})}{x y^{11}}}$

Cancel the common factors.

Factor $x$ out of $x y^{11}$ .

$\sqrt{\frac{x (9 x^{14} y^{9})}{x (y^{11})}}$

Cancel the common factor.

$\sqrt{\frac{x (9 x^{14} y^{9})}{x y^{11}}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{14} y^{9}}{y^{11}}}$

Step 3

Cancel the common factor of $y^{9}$ and $y^{11}$ .

Factor $y^{9}$ out of $9 x^{14} y^{9}$ .

$\sqrt{\frac{y^{9} (9 x^{14})}{y^{11}}}$

Cancel the common factors.

Factor $y^{9}$ out of $y^{11}$ .

$\sqrt{\frac{y^{9} (9 x^{14})}{y^{9} y^{2}}}$

Cancel the common factor.

$\sqrt{\frac{y^{9} (9 x^{14})}{y^{9} y^{2}}}$

Rewrite the expression.

$\sqrt{\frac{9 x^{14}}{y^{2}}}$

Step 4

Rewrite $9 x^{14}$ as ${(3 x^{7})}^{2}$ .

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

Step 5

Rewrite $\frac{{(3 x^{7})}^{2}}{y^{2}}$ as ${(\frac{3 x^{7}}{y})}^{2}$ .

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

Step 6

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

$\frac{3 x^{7}}{y}$