Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

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

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Step 1.1.1

Rewrite $4$ as $2^{2}$ .

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

Step 1.1.2

Factor out $y^{4}$ .

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

Step 1.1.3

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

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

Step 1.1.4

Move $x$ .

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

Step 1.1.5

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

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

Step 1.1.6

Add parentheses.

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

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

Step 1.2

Pull terms out from under the radical.

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

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Cancel the common factors.

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Step 2.2.1

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

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

Step 2.2.2

Cancel the common factor.

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

Step 2.2.3

Rewrite the expression.

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

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

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

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$