Algebra Examples

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

Step 1

Simplify the numerator.

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Step 1.1

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.1.1

Factor $9$ out of $27$ .

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

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

$\frac{\sqrt{3^{2} \cdot 3}}{\sqrt{3^{3}}}$

$\frac{\sqrt{3^{2} \cdot 3}}{\sqrt{3^{3}}}$

Step 1.2

Pull terms out from under the radical.

$\frac{3 \sqrt{3}}{\sqrt{3^{3}}}$

$\frac{3 \sqrt{3}}{\sqrt{3^{3}}}$

Step 2

Simplify the denominator.

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Step 2.1

Raise $3$ to the power of $3$ .

$\frac{3 \sqrt{3}}{\sqrt{27}}$

Step 2.2

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 2.2.1

Factor $9$ out of $27$ .

$\frac{3 \sqrt{3}}{\sqrt{9 (3)}}$

Step 2.2.2

Rewrite $9$ as $3^{2}$ .

$\frac{3 \sqrt{3}}{\sqrt{3^{2} \cdot 3}}$

$\frac{3 \sqrt{3}}{\sqrt{3^{2} \cdot 3}}$

Step 2.3

Pull terms out from under the radical.

$\frac{3 \sqrt{3}}{3 \sqrt{3}}$

$\frac{3 \sqrt{3}}{3 \sqrt{3}}$

Step 3

Reduce the expression by cancelling the common factors.

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Step 3.1

Cancel the common factor of $3$ .

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Step 3.1.1

Cancel the common factor.

$\frac{3 \sqrt{3}}{3 \sqrt{3}}$

Step 3.1.2

Rewrite the expression.

$\frac{\sqrt{3}}{\sqrt{3}}$

$\frac{\sqrt{3}}{\sqrt{3}}$

Step 3.2

Cancel the common factor of $\sqrt{3}$ .

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Step 3.2.1

Cancel the common factor.

$\frac{\sqrt{3}}{\sqrt{3}}$

Step 3.2.2

Rewrite the expression.

$1$

$1$

$1$

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