Precalculus Examples

$\frac{\sqrt{125 x^{5} y^{6}}}{\sqrt{5 x^{3} y^{10}}}$

Step 1

Combine $\sqrt{125 x^{5} y^{6}}$ and $\sqrt{5 x^{3} y^{10}}$ into a single radical.

$\sqrt{\frac{125 x^{5} y^{6}}{5 x^{3} y^{10}}}$

Step 2

Reduce the expression $\frac{125 x^{5} y^{6}}{5 x^{3} y^{10}}$ by cancelling the common factors.

Tap for more steps...

Step 2.1

Factor $5$ out of $125 x^{5} y^{6}$ .

$\sqrt{\frac{5 (25 x^{5} y^{6})}{5 x^{3} y^{10}}}$

Step 2.2

Factor $5$ out of $5 x^{3} y^{10}$ .

$\sqrt{\frac{5 (25 x^{5} y^{6})}{5 (x^{3} y^{10})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{5 (25 x^{5} y^{6})}{5 (x^{3} y^{10})}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{25 x^{5} y^{6}}{x^{3} y^{10}}}$

Step 3

Cancel the common factor of $x^{5}$ and $x^{3}$ .

Tap for more steps...

Step 3.1

Factor $x^{3}$ out of $25 x^{5} y^{6}$ .

$\sqrt{\frac{x^{3} (25 x^{2} y^{6})}{x^{3} y^{10}}}$

Step 3.2

Cancel the common factors.

Tap for more steps...

Step 3.2.1

Factor $x^{3}$ out of $x^{3} y^{10}$ .

$\sqrt{\frac{x^{3} (25 x^{2} y^{6})}{x^{3} (y^{10})}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{x^{3} (25 x^{2} y^{6})}{x^{3} y^{10}}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{25 x^{2} y^{6}}{y^{10}}}$

Step 4

Cancel the common factor of $y^{6}$ and $y^{10}$ .

Tap for more steps...

Step 4.1

Factor $y^{6}$ out of $25 x^{2} y^{6}$ .

$\sqrt{\frac{y^{6} (25 x^{2})}{y^{10}}}$

Step 4.2

Cancel the common factors.

Tap for more steps...

Step 4.2.1

Factor $y^{6}$ out of $y^{10}$ .

$\sqrt{\frac{y^{6} (25 x^{2})}{y^{6} y^{4}}}$

Step 4.2.2

Cancel the common factor.

$\sqrt{\frac{y^{6} (25 x^{2})}{y^{6} y^{4}}}$

Step 4.2.3

Rewrite the expression.

$\sqrt{\frac{25 x^{2}}{y^{4}}}$

Step 5

Rewrite $25 x^{2}$ as ${(5 x)}^{2}$ .

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

Step 6

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

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

Step 7

Rewrite $\frac{{(5 x)}^{2}}{{(y^{2})}^{2}}$ as ${(\frac{5 x}{y^{2}})}^{2}$ .

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

Step 8

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

$\frac{5 x}{y^{2}}$