Algebra Examples

$\frac{\sqrt{x^{11} y^{5}}}{\sqrt{x y}}$

Step 1

Combine $\sqrt{x^{11} y^{5}}$ and $\sqrt{x y}$ into a single radical.

$\sqrt{\frac{x^{11} y^{5}}{x y}}$

Step 2

Reduce the expression $\frac{x^{11} y^{5}}{x y}$ by cancelling the common factors.

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Step 2.1

Factor $x$ out of $x^{11} y^{5}$ .

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

Step 2.2

Factor $x$ out of $x y$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

$\sqrt{\frac{x^{10} y^{5}}{y}}$

Step 3

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

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Step 3.1

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

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Raise $y$ to the power of $1$ .

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

Step 3.2.2

Factor $y$ out of $y^{1}$ .

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

Step 3.2.3

Cancel the common factor.

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

Step 3.2.4

Rewrite the expression.

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

Step 3.2.5

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

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

Step 4

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

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

Step 5

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

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