Algebra Examples

$\frac{4 x^{6} y^{4} \sqrt{5 x y}}{4 x^{4} y^{2} \sqrt{5}}$

Step 1

Cancel the common factor of $4$ .

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Step 1.1

Cancel the common factor.

$\frac{4 x^{6} y^{4} \sqrt{5 x y}}{4 x^{4} y^{2} \sqrt{5}}$

Step 1.2

Rewrite the expression.

$\frac{x^{6} y^{4} \sqrt{5 x y}}{x^{4} y^{2} \sqrt{5}}$

Step 2

Cancel the common factor of $x^{6}$ and $x^{4}$ .

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Step 2.1

Factor $x^{4}$ out of $x^{6} y^{4} \sqrt{5 x y}$ .

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $x^{4}$ out of $x^{4} y^{2} \sqrt{5}$ .

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

Step 3

Cancel the common factor of $y^{4}$ and $y^{2}$ .

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Step 3.1

Factor $y^{2}$ out of $x^{2} y^{4} \sqrt{5 x y}$ .

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

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $y^{2}$ out of $y^{2} \sqrt{5}$ .

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

Step 3.2.2

Cancel the common factor.

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

Step 3.2.3

Rewrite the expression.

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

Step 4

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

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

Step 5

Reduce the expression by cancelling the common factors.

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Step 5.1

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

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Step 5.1.1

Cancel the common factor.

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

Step 5.1.2

Rewrite the expression.

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

Step 5.2

Divide $x y$ by $1$ .

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