Algebra Examples

$2 \sqrt{27} - 3 \sqrt{48} + \frac{1}{5} \sqrt{75}$

Step 1

Simplify each term.

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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 $27$ .

$2 \sqrt{9 (3)} - 3 \sqrt{48} + \frac{1}{5} \cdot \sqrt{75}$

Step 1.1.2

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

$2 \sqrt{3^{2} \cdot 3} - 3 \sqrt{48} + \frac{1}{5} \cdot \sqrt{75}$

Step 1.2

Pull terms out from under the radical.

$2 (3 \sqrt{3}) - 3 \sqrt{48} + \frac{1}{5} \cdot \sqrt{75}$

Step 1.3

Multiply $3$ by $2$ .

$6 \sqrt{3} - 3 \sqrt{48} + \frac{1}{5} \cdot \sqrt{75}$

Step 1.4

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 1.4.1

Factor $16$ out of $48$ .

$6 \sqrt{3} - 3 \sqrt{16 (3)} + \frac{1}{5} \cdot \sqrt{75}$

Step 1.4.2

Rewrite $16$ as $4^{2}$ .

$6 \sqrt{3} - 3 \sqrt{4^{2} \cdot 3} + \frac{1}{5} \cdot \sqrt{75}$

Step 1.5

Pull terms out from under the radical.

$6 \sqrt{3} - 3 (4 \sqrt{3}) + \frac{1}{5} \cdot \sqrt{75}$

Step 1.6

Multiply $4$ by $- 3$ .

$6 \sqrt{3} - 12 \sqrt{3} + \frac{1}{5} \cdot \sqrt{75}$

Step 1.7

Rewrite $75$ as $5^{2} \cdot 3$ .

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Step 1.7.1

Factor $25$ out of $75$ .

$6 \sqrt{3} - 12 \sqrt{3} + \frac{1}{5} \cdot \sqrt{25 (3)}$

Step 1.7.2

Rewrite $25$ as $5^{2}$ .

$6 \sqrt{3} - 12 \sqrt{3} + \frac{1}{5} \cdot \sqrt{5^{2} \cdot 3}$

Step 1.8

Pull terms out from under the radical.

$6 \sqrt{3} - 12 \sqrt{3} + \frac{1}{5} \cdot (5 \sqrt{3})$

Step 1.9

Cancel the common factor of $5$ .

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Step 1.9.1

Factor $5$ out of $5 \sqrt{3}$ .

$6 \sqrt{3} - 12 \sqrt{3} + \frac{1}{5} \cdot (5 (\sqrt{3}))$

Step 1.9.2

Cancel the common factor.

$6 \sqrt{3} - 12 \sqrt{3} + \frac{1}{5} \cdot (5 \sqrt{3})$

Step 1.9.3

Rewrite the expression.

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $12 \sqrt{3}$ from $6 \sqrt{3}$ .

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

Step 2.2

Add $- 6 \sqrt{3}$ and $\sqrt{3}$ .

$- 5 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 5 \sqrt{3}$

Decimal Form:

$- 8.66025403 \dots$