Algebra Examples

$\frac{\sqrt{27 x^{5}}}{\sqrt{3 x^{3}}}$

Step 1

Combine $\sqrt{27 x^{5}}$ and $\sqrt{3 x^{3}}$ into a single radical.

$\sqrt{\frac{27 x^{5}}{3 x^{3}}}$

Step 2

Reduce the expression $\frac{27 x^{5}}{3 x^{3}}$ by cancelling the common factors.

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Step 2.1

Factor $3$ out of $27 x^{5}$ .

$\sqrt{\frac{3 (9 x^{5})}{3 x^{3}}}$

Step 2.2

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

$\sqrt{\frac{3 (9 x^{5})}{3 (x^{3})}}$

Step 2.3

Cancel the common factor.

$\sqrt{\frac{3 (9 x^{5})}{3 x^{3}}}$

Step 2.4

Rewrite the expression.

$\sqrt{\frac{9 x^{5}}{x^{3}}}$

Step 3

Cancel the common factor of $x^{5}$ and $x^{3}$ .

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Step 3.1

Factor $x^{3}$ out of $9 x^{5}$ .

$\sqrt{\frac{x^{3} (9 x^{2})}{x^{3}}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\sqrt{\frac{x^{3} (9 x^{2})}{x^{3} \cdot 1}}$

Step 3.2.2

Cancel the common factor.

$\sqrt{\frac{x^{3} (9 x^{2})}{x^{3} \cdot 1}}$

Step 3.2.3

Rewrite the expression.

$\sqrt{\frac{9 x^{2}}{1}}$

Step 3.2.4

Divide $9 x^{2}$ by $1$ .

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

Step 4

Rewrite $9 x^{2}$ as ${(3 x)}^{2}$ .

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

Step 5

Pull terms out from under the radical.

$| 3 x |$

Step 6

Remove non-negative terms from the absolute value.

$3 | x |$