Pre-Algebra Examples

$\frac{\sqrt{96 x^{3}}}{8 x}$

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $96 x^{3}$ as ${(4 x)}^{2} \cdot (6 x)$ .

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Step 1.1.1

Factor $16$ out of $96$ .

$\frac{\sqrt{16 (6) x^{3}}}{8 x}$

Step 1.1.2

Rewrite $16$ as $4^{2}$ .

$\frac{\sqrt{4^{2} \cdot 6 x^{3}}}{8 x}$

Step 1.1.3

Factor out $x^{2}$ .

$\frac{\sqrt{4^{2} \cdot 6 (x^{2} x)}}{8 x}$

Step 1.1.4

Move $6$ .

$\frac{\sqrt{4^{2} x^{2} \cdot 6 x}}{8 x}$

Step 1.1.5

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

$\frac{\sqrt{{(4 x)}^{2} \cdot 6 x}}{8 x}$

Step 1.1.6

Add parentheses.

$\frac{\sqrt{{(4 x)}^{2} \cdot (6 x)}}{8 x}$

$\frac{\sqrt{{(4 x)}^{2} \cdot (6 x)}}{8 x}$

Step 1.2

Pull terms out from under the radical.

$\frac{4 x \sqrt{6 x}}{8 x}$

$\frac{4 x \sqrt{6 x}}{8 x}$

Step 2

Cancel the common factor of $4$ and $8$ .

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Step 2.1

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

$\frac{4 (x \sqrt{6 x})}{8 x}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $4$ out of $8 x$ .

$\frac{4 (x \sqrt{6 x})}{4 (2 x)}$

Step 2.2.2

Cancel the common factor.

$\frac{4 (x \sqrt{6 x})}{4 (2 x)}$

Step 2.2.3

Rewrite the expression.

$\frac{x \sqrt{6 x}}{2 x}$

$\frac{x \sqrt{6 x}}{2 x}$

$\frac{x \sqrt{6 x}}{2 x}$

Step 3

Cancel the common factor of $x$ .

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Step 3.1

Cancel the common factor.

$\frac{x \sqrt{6 x}}{2 x}$

Step 3.2

Rewrite the expression.

$\frac{\sqrt{6 x}}{2}$

$\frac{\sqrt{6 x}}{2}$

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