Algebra Examples

$\frac{\sqrt[3]{9 x^{2}}}{\sqrt[3]{3 x}}$

Step 1

Combine $\sqrt[3]{9 x^{2}}$ and $\sqrt[3]{3 x}$ into a single radical.

$\sqrt[3]{\frac{9 x^{2}}{3 x}}$

Step 2

Reduce the expression $\frac{9 x^{2}}{3 x}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $9 x^{2}$ .

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

Step 2.2

Factor $3$ out of $3 x$ .

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

Step 2.3

Cancel the common factor.

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

Step 2.4

Rewrite the expression.

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

Step 3

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

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Step 3.1

Factor $x$ out of $3 x^{2}$ .

$\sqrt[3]{\frac{x (3 x)}{x}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Raise $x$ to the power of $1$ .

$\sqrt[3]{\frac{x (3 x)}{x^{1}}}$

Step 3.2.2

Factor $x$ out of $x^{1}$ .

$\sqrt[3]{\frac{x (3 x)}{x \cdot 1}}$

Step 3.2.3

Cancel the common factor.

$\sqrt[3]{\frac{x (3 x)}{x \cdot 1}}$

Step 3.2.4

Rewrite the expression.

$\sqrt[3]{\frac{3 x}{1}}$

Step 3.2.5

Divide $3 x$ by $1$ .

$\sqrt[3]{3 x}$