Simplify the Radical Expression square root of (25x^9y^3)/(64x^6y^11)

$\sqrt{\frac{25 x^{9} y^{3}}{64 x^{6} y^{11}}}$

Step 1

Reduce the expression $\frac{25 x^{9} y^{3}}{64 x^{6} y^{11}}$ by cancelling the common factors.

Factor $x^{6}$ out of $25 x^{9} y^{3}$ .

$\sqrt{\frac{x^{6} (25 x^{3} y^{3})}{64 x^{6} y^{11}}}$

Factor $x^{6}$ out of $64 x^{6} y^{11}$ .

$\sqrt{\frac{x^{6} (25 x^{3} y^{3})}{x^{6} (64 y^{11})}}$

Cancel the common factor.

$\sqrt{\frac{x^{6} (25 x^{3} y^{3})}{x^{6} (64 y^{11})}}$

Rewrite the expression.

$\sqrt{\frac{25 x^{3} y^{3}}{64 y^{11}}}$

Step 2

Cancel the common factor of $y^{3}$ and $y^{11}$ .

Factor $y^{3}$ out of $25 x^{3} y^{3}$ .

$\sqrt{\frac{y^{3} (25 x^{3})}{64 y^{11}}}$

Cancel the common factors.

Factor $y^{3}$ out of $64 y^{11}$ .

$\sqrt{\frac{y^{3} (25 x^{3})}{y^{3} (64 y^{8})}}$

Cancel the common factor.

$\sqrt{\frac{y^{3} (25 x^{3})}{y^{3} (64 y^{8})}}$

Rewrite the expression.

$\sqrt{\frac{25 x^{3}}{64 y^{8}}}$

Step 3

Rewrite $\frac{25 x^{3}}{64 y^{8}}$ as ${(\frac{5 x}{8 y^{4}})}^{2} x$ .

Factor the perfect power ${(5 x)}^{2}$ out of $25 x^{3}$ .

$\sqrt{\frac{{(5 x)}^{2} x}{64 y^{8}}}$

Factor the perfect power ${(8 y^{4})}^{2}$ out of $64 y^{8}$ .

$\sqrt{\frac{{(5 x)}^{2} x}{{(8 y^{4})}^{2} \cdot 1}}$

Rearrange the fraction $\frac{{(5 x)}^{2} x}{{(8 y^{4})}^{2} \cdot 1}$ .

$\sqrt{{(\frac{5 x}{8 y^{4}})}^{2} x}$

Step 4

Pull terms out from under the radical.

$| \frac{5 x}{8 y^{4}} | \sqrt{x}$

Step 5

Remove non-negative terms from the absolute value.

$\frac{5 | x |}{8 y^{4}} \sqrt{x}$

Step 6

Combine $\frac{5 | x |}{8 y^{4}}$ and $\sqrt{x}$ .

$\frac{5 | x | \sqrt{x}}{8 y^{4}}$