Algebra Examples

$\frac{\sqrt{12 x}}{2 x^{2}}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $12 x$ as $2^{2} \cdot (3 x)$ .

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Step 1.1.1

Factor $4$ out of $12$ .

$\frac{\sqrt{4 (3) x}}{2 x^{2}}$

Step 1.1.2

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

$\frac{\sqrt{2^{2} \cdot 3 x}}{2 x^{2}}$

Step 1.1.3

Add parentheses.

$\frac{\sqrt{2^{2} \cdot (3 x)}}{2 x^{2}}$

$\frac{\sqrt{2^{2} \cdot (3 x)}}{2 x^{2}}$

Step 1.2

Pull terms out from under the radical.

$\frac{2 \sqrt{3 x}}{2 x^{2}}$

$\frac{2 \sqrt{3 x}}{2 x^{2}}$

Step 2

Cancel the common factor of $2$ .

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Step 2.1

Cancel the common factor.

$\frac{2 \sqrt{3 x}}{2 x^{2}}$

Step 2.2

Rewrite the expression.

$\frac{\sqrt{3 x}}{x^{2}}$

$\frac{\sqrt{3 x}}{x^{2}}$

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