Algebra Examples

$\frac{\sqrt{x^{12}}}{\sqrt{x^{5}}}$

Step 1

Combine $\sqrt{x^{12}}$ and $\sqrt{x^{5}}$ into a single radical.

$\sqrt{\frac{x^{12}}{x^{5}}}$

Step 2

Reduce the expression by cancelling the common factors.

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Step 2.1

Reduce the expression $\frac{x^{12}}{x^{5}}$ by cancelling the common factors.

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Step 2.1.1

Factor $x^{5}$ out of $x^{12}$ .

$\sqrt{\frac{x^{5} x^{7}}{x^{5}}}$

Step 2.1.2

Multiply by $1$ .

$\sqrt{\frac{x^{5} x^{7}}{x^{5} \cdot 1}}$

Step 2.1.3

Cancel the common factor.

$\sqrt{\frac{x^{5} x^{7}}{x^{5} \cdot 1}}$

Step 2.1.4

Rewrite the expression.

$\sqrt{\frac{x^{7}}{1}}$

Step 2.2

Divide $x^{7}$ by $1$ .

$\sqrt{x^{7}}$

Step 3

Rewrite $x^{7}$ as ${(x^{3})}^{2} x$ .

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Step 3.1

Factor out $x^{6}$ .

$\sqrt{x^{6} x}$

Step 3.2

Rewrite $x^{6}$ as ${(x^{3})}^{2}$ .

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

Step 4

Pull terms out from under the radical.

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