Algebra Examples

$\frac{2 \sqrt{27} - 3 \sqrt{12} + \sqrt{24}}{\sqrt{3}}$

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 $27$ .

$\frac{2 \sqrt{9 (3)} - 3 \sqrt{12} + \sqrt{24}}{\sqrt{3}}$

Step 1.1.2

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

$\frac{2 \sqrt{3^{2} \cdot 3} - 3 \sqrt{12} + \sqrt{24}}{\sqrt{3}}$

Step 1.2

Pull terms out from under the radical.

$\frac{2 (3 \sqrt{3}) - 3 \sqrt{12} + \sqrt{24}}{\sqrt{3}}$

Step 1.3

Multiply $3$ by $2$ .

$\frac{6 \sqrt{3} - 3 \sqrt{12} + \sqrt{24}}{\sqrt{3}}$

Step 1.4

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

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Step 1.4.1

Factor $4$ out of $12$ .

$\frac{6 \sqrt{3} - 3 \sqrt{4 (3)} + \sqrt{24}}{\sqrt{3}}$

Step 1.4.2

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

$\frac{6 \sqrt{3} - 3 \sqrt{2^{2} \cdot 3} + \sqrt{24}}{\sqrt{3}}$

Step 1.5

Pull terms out from under the radical.

$\frac{6 \sqrt{3} - 3 (2 \sqrt{3}) + \sqrt{24}}{\sqrt{3}}$

Step 1.6

Multiply $2$ by $- 3$ .

$\frac{6 \sqrt{3} - 6 \sqrt{3} + \sqrt{24}}{\sqrt{3}}$

Step 1.7

Rewrite $24$ as $2^{2} \cdot 6$ .

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Step 1.7.1

Factor $4$ out of $24$ .

$\frac{6 \sqrt{3} - 6 \sqrt{3} + \sqrt{4 (6)}}{\sqrt{3}}$

Step 1.7.2

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

$\frac{6 \sqrt{3} - 6 \sqrt{3} + \sqrt{2^{2} \cdot 6}}{\sqrt{3}}$

Step 1.8

Pull terms out from under the radical.

$\frac{6 \sqrt{3} - 6 \sqrt{3} + 2 \sqrt{6}}{\sqrt{3}}$

Step 1.9

Subtract $6 \sqrt{3}$ from $6 \sqrt{3}$ .

$\frac{0 + 2 \sqrt{6}}{\sqrt{3}}$

Step 1.10

Add $0$ and $2 \sqrt{6}$ .

$\frac{2 \sqrt{6}}{\sqrt{3}}$

Step 2

Combine $\sqrt{6}$ and $\sqrt{3}$ into a single radical.

$2 \sqrt{\frac{6}{3}}$

Step 3

Divide $6$ by $3$ .

$2 \sqrt{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$