Simplify square root of (128x^5y^6)/(2x^7y^5)

$\sqrt{\frac{128 x^{5} y^{6}}{2 x^{7} y^{5}}}$

Step 1

Reduce the expression $\frac{128 x^{5} y^{6}}{2 x^{7} y^{5}}$ by cancelling the common factors.

Factor $2$ out of $128 x^{5} y^{6}$ .

$\sqrt{\frac{2 (64 x^{5} y^{6})}{2 x^{7} y^{5}}}$

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

$\sqrt{\frac{2 (64 x^{5} y^{6})}{2 (x^{7} y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{2 (64 x^{5} y^{6})}{2 (x^{7} y^{5})}}$

Rewrite the expression.

$\sqrt{\frac{64 x^{5} y^{6}}{x^{7} y^{5}}}$

Step 2

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

Factor $x^{5}$ out of $64 x^{5} y^{6}$ .

$\sqrt{\frac{x^{5} (64 y^{6})}{x^{7} y^{5}}}$

Cancel the common factors.

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

$\sqrt{\frac{x^{5} (64 y^{6})}{x^{5} (x^{2} y^{5})}}$

Cancel the common factor.

$\sqrt{\frac{x^{5} (64 y^{6})}{x^{5} (x^{2} y^{5})}}$

Rewrite the expression.

$\sqrt{\frac{64 y^{6}}{x^{2} y^{5}}}$

Step 3

Cancel the common factor of $y^{6}$ and $y^{5}$ .

Factor $y^{5}$ out of $64 y^{6}$ .

$\sqrt{\frac{y^{5} (64 y)}{x^{2} y^{5}}}$

Cancel the common factors.

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

$\sqrt{\frac{y^{5} (64 y)}{y^{5} x^{2}}}$

Cancel the common factor.

$\sqrt{\frac{y^{5} (64 y)}{y^{5} x^{2}}}$

Rewrite the expression.

$\sqrt{\frac{64 y}{x^{2}}}$

Step 4

Rewrite $\frac{64 y}{x^{2}}$ as ${(\frac{8}{x})}^{2} y$ .

Factor the perfect power $8^{2}$ out of $64 y$ .

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

Factor the perfect power $x^{2}$ out of $x^{2}$ .

$\sqrt{\frac{8^{2} y}{x^{2} \cdot 1}}$

Rearrange the fraction $\frac{8^{2} y}{x^{2} \cdot 1}$ .

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

Step 5

Pull terms out from under the radical.

$\frac{8}{x} \sqrt{y}$

Step 6

Combine $\frac{8}{x}$ and $\sqrt{y}$ .

$\frac{8 \sqrt{y}}{x}$

Simplify square root of (128x^5y^6)/(2x^7y^5)

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