Simplify ( square root of 12x^30y^23)/( square root of 3x^2y^13)

$\frac{\sqrt{12 x^{30} y^{23}}}{\sqrt{3 x^{2} y^{13}}}$

Combine $\sqrt{12 x^{30} y^{23}}$ and $\sqrt{3 x^{2} y^{13}}$ into a single radical.

$\sqrt{\frac{12 x^{30} y^{23}}{3 x^{2} y^{13}}}$

Reduce the expression $\frac{12 x^{30} y^{23}}{3 x^{2} y^{13}}$ by cancelling the common factors.

Factor $3$ out of $12 x^{30} y^{23}$ .

$\sqrt{\frac{3 (4 x^{30} y^{23})}{3 x^{2} y^{13}}}$

Factor $3$ out of $3 x^{2} y^{13}$ .

$\sqrt{\frac{3 (4 x^{30} y^{23})}{3 (x^{2} y^{13})}}$

Cancel the common factor.

$\sqrt{\frac{3 (4 x^{30} y^{23})}{3 (x^{2} y^{13})}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{30} y^{23}}{x^{2} y^{13}}}$

Cancel the common factor of $x^{30}$ and $x^{2}$ .

Factor $x^{2}$ out of $4 x^{30} y^{23}$ .

$\sqrt{\frac{x^{2} (4 x^{28} y^{23})}{x^{2} y^{13}}}$

Cancel the common factors.

Factor $x^{2}$ out of $x^{2} y^{13}$ .

$\sqrt{\frac{x^{2} (4 x^{28} y^{23})}{x^{2} (y^{13})}}$

Cancel the common factor.

$\sqrt{\frac{x^{2} (4 x^{28} y^{23})}{x^{2} y^{13}}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{28} y^{23}}{y^{13}}}$

Cancel the common factor of $y^{23}$ and $y^{13}$ .

Factor $y^{13}$ out of $4 x^{28} y^{23}$ .

$\sqrt{\frac{y^{13} (4 x^{28} y^{10})}{y^{13}}}$

Cancel the common factors.

Multiply by $1$ .

$\sqrt{\frac{y^{13} (4 x^{28} y^{10})}{y^{13} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y^{13} (4 x^{28} y^{10})}{y^{13} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{4 x^{28} y^{10}}{1}}$

Divide $4 x^{28} y^{10}$ by $1$ .

$\sqrt{4 x^{28} y^{10}}$

Rewrite $4 x^{28} y^{10}$ as ${(2 x^{14} y^{5})}^{2}$ .

$\sqrt{{(2 x^{14} y^{5})}^{2}}$

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

$2 x^{14} y^{5}$