Algebra Examples

$\frac{\sqrt{27} + \sqrt{12}}{\sqrt{3}}$

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 $27$ .

$\frac{\sqrt{9 (3)} + \sqrt{12}}{\sqrt{3}}$

Step 1.1.2

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

$\frac{\sqrt{3^{2} \cdot 3} + \sqrt{12}}{\sqrt{3}}$

Step 1.2

Pull terms out from under the radical.

$\frac{3 \sqrt{3} + \sqrt{12}}{\sqrt{3}}$

Step 1.3

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.3.1

Factor $4$ out of $12$ .

$\frac{3 \sqrt{3} + \sqrt{4 (3)}}{\sqrt{3}}$

Step 1.3.2

Rewrite $4$ as $2^{2}$ .

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

Step 1.4

Pull terms out from under the radical.

$\frac{3 \sqrt{3} + 2 \sqrt{3}}{\sqrt{3}}$

Step 1.5

Add $3 \sqrt{3}$ and $2 \sqrt{3}$ .

$\frac{5 \sqrt{3}}{\sqrt{3}}$

Step 2

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

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Step 2.1

Cancel the common factor.

$\frac{5 \sqrt{3}}{\sqrt{3}}$

Step 2.2

Divide $5$ by $1$ .

$5$