Algebra Examples

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

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

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

Step 5

Cancel the common factor of $2 y$ .

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Step 5.1

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

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

Step 5.2

Cancel the common factor.

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

Step 5.3

Rewrite the expression.

$y x^{2}$