Simplify ( square root of 20x^7y^10)/( square root of y^2)

$\frac{\sqrt{20 x^{7} y^{10}}}{\sqrt{y^{2}}}$

Combine $\sqrt{20 x^{7} y^{10}}$ and $\sqrt{y^{2}}$ into a single radical.

$\sqrt{\frac{20 x^{7} y^{10}}{y^{2}}}$

Reduce the expression by cancelling the common factors.

Reduce the expression $\frac{20 x^{7} y^{10}}{y^{2}}$ by cancelling the common factors.

Factor $y^{2}$ out of $20 x^{7} y^{10}$ .

$\sqrt{\frac{y^{2} (20 x^{7} y^{8})}{y^{2}}}$

Multiply by $1$ .

$\sqrt{\frac{y^{2} (20 x^{7} y^{8})}{y^{2} \cdot 1}}$

Cancel the common factor.

$\sqrt{\frac{y^{2} (20 x^{7} y^{8})}{y^{2} \cdot 1}}$

Rewrite the expression.

$\sqrt{\frac{20 x^{7} y^{8}}{1}}$

Divide $20 x^{7} y^{8}$ by $1$ .

$\sqrt{20 x^{7} y^{8}}$

Rewrite $20 x^{7} y^{8}$ as ${(2 x^{3} y^{4})}^{2} \cdot (5 x)$ .

Factor $4$ out of $20$ .

$\sqrt{4 (5) x^{7} y^{8}}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 5 x^{7} y^{8}}$

Factor out $x^{6}$ .

$\sqrt{2^{2} \cdot 5 (x^{6} x) y^{8}}$

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

$\sqrt{2^{2} \cdot 5 ({(x^{3})}^{2} x) y^{8}}$

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

$\sqrt{2^{2} \cdot 5 ({(x^{3})}^{2} x) {(y^{4})}^{2}}$

Move $x$ .

$\sqrt{2^{2} \cdot 5 ({(x^{3})}^{2}) {(y^{4})}^{2} x}$

Move $5$ .

$\sqrt{(2^{2} ({(x^{3})}^{2})) {(y^{4})}^{2} \cdot 5 x}$

Rewrite $(2^{2} ({(x^{3})}^{2})) {(y^{4})}^{2}$ as ${(2 x^{3} y^{4})}^{2}$ .

$\sqrt{{(2 x^{3} y^{4})}^{2} \cdot 5 x}$

Add parentheses.

$\sqrt{{(2 x^{3} y^{4})}^{2} \cdot (5 x)}$

Pull terms out from under the radical.

$2 x^{3} y^{4} \sqrt{5 x}$