Algebra Examples

$\frac{\sqrt{2 x^{9}}}{\sqrt{x^{6}}}$

Step 1

Combine $\sqrt{2 x^{9}}$ and $\sqrt{x^{6}}$ into a single radical.

$\sqrt{\frac{2 x^{9}}{x^{6}}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{2 x^{9}}{x^{6}}$ by cancelling the common factors.

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Step 2.1.1

Factor $x^{6}$ out of $2 x^{9}$ .

$\sqrt{\frac{x^{6} (2 x^{3})}{x^{6}}}$

Step 2.1.2

Multiply by $1$ .

$\sqrt{\frac{x^{6} (2 x^{3})}{x^{6} \cdot 1}}$

Step 2.1.3

Cancel the common factor.

$\sqrt{\frac{x^{6} (2 x^{3})}{x^{6} \cdot 1}}$

Step 2.1.4

Rewrite the expression.

$\sqrt{\frac{2 x^{3}}{1}}$

Step 2.2

Divide $2 x^{3}$ by $1$ .

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

Step 3

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

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Step 3.1

Factor out $x^{2}$ .

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

Step 3.2

Reorder $2$ and $x^{2}$ .

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

Step 3.3

Add parentheses.

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

Step 4

Pull terms out from under the radical.

$x \sqrt{2 x}$