Basic Math Examples

$\frac{1}{4} \cdot \sqrt{192} - \frac{2}{3} \cdot \sqrt{75} + \frac{1}{7} \cdot \sqrt{147}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $192$ as $8^{2} \cdot 3$ .

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Step 1.1.1

Factor $64$ out of $192$ .

$\frac{1}{4} \cdot \sqrt{64 (3)} - \frac{2}{3} \cdot \sqrt{75} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.1.2

Rewrite $64$ as $8^{2}$ .

$\frac{1}{4} \cdot \sqrt{8^{2} \cdot 3} - \frac{2}{3} \cdot \sqrt{75} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.2

Pull terms out from under the radical.

$\frac{1}{4} \cdot (8 \sqrt{3}) - \frac{2}{3} \cdot \sqrt{75} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Factor $4$ out of $8 \sqrt{3}$ .

$\frac{1}{4} \cdot (4 (2 \sqrt{3})) - \frac{2}{3} \cdot \sqrt{75} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.3.2

Cancel the common factor.

$\frac{1}{4} \cdot (4 (2 \sqrt{3})) - \frac{2}{3} \cdot \sqrt{75} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.3.3

Rewrite the expression.

$2 \sqrt{3} - \frac{2}{3} \cdot \sqrt{75} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.4

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

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Step 1.4.1

Factor $25$ out of $75$ .

$2 \sqrt{3} - \frac{2}{3} \cdot \sqrt{25 (3)} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.4.2

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

$2 \sqrt{3} - \frac{2}{3} \cdot \sqrt{5^{2} \cdot 3} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.5

Pull terms out from under the radical.

$2 \sqrt{3} - \frac{2}{3} \cdot (5 \sqrt{3}) + \frac{1}{7} \cdot \sqrt{147}$

Step 1.6

Multiply $- \frac{2}{3} (5 \sqrt{3})$ .

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Step 1.6.1

Multiply $5$ by $- 1$ .

$2 \sqrt{3} - 5 (\frac{2}{3}) \sqrt{3} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.6.2

Combine $- 5$ and $\frac{2}{3}$ .

$2 \sqrt{3} + \frac{- 5 \cdot 2}{3} \sqrt{3} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.6.3

Multiply $- 5$ by $2$ .

$2 \sqrt{3} + \frac{- 10}{3} \sqrt{3} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.6.4

Combine $\frac{- 10}{3}$ and $\sqrt{3}$ .

$2 \sqrt{3} + \frac{- 10 \sqrt{3}}{3} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.7

Move the negative in front of the fraction.

$2 \sqrt{3} - \frac{10 \sqrt{3}}{3} + \frac{1}{7} \cdot \sqrt{147}$

Step 1.8

Rewrite $147$ as $7^{2} \cdot 3$ .

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Step 1.8.1

Factor $49$ out of $147$ .

$2 \sqrt{3} - \frac{10 \sqrt{3}}{3} + \frac{1}{7} \cdot \sqrt{49 (3)}$

Step 1.8.2

Rewrite $49$ as $7^{2}$ .

$2 \sqrt{3} - \frac{10 \sqrt{3}}{3} + \frac{1}{7} \cdot \sqrt{7^{2} \cdot 3}$

Step 1.9

Pull terms out from under the radical.

$2 \sqrt{3} - \frac{10 \sqrt{3}}{3} + \frac{1}{7} \cdot (7 \sqrt{3})$

Step 1.10

Cancel the common factor of $7$ .

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Step 1.10.1

Factor $7$ out of $7 \sqrt{3}$ .

$2 \sqrt{3} - \frac{10 \sqrt{3}}{3} + \frac{1}{7} \cdot (7 (\sqrt{3}))$

Step 1.10.2

Cancel the common factor.

$2 \sqrt{3} - \frac{10 \sqrt{3}}{3} + \frac{1}{7} \cdot (7 \sqrt{3})$

Step 1.10.3

Rewrite the expression.

$2 \sqrt{3} - \frac{10 \sqrt{3}}{3} + \sqrt{3}$

Step 2

Find the common denominator.

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Step 2.1

Write $2 \sqrt{3}$ as a fraction with denominator $1$ .

$\frac{2 \sqrt{3}}{1} - \frac{10 \sqrt{3}}{3} + \sqrt{3}$

Step 2.2

Multiply $\frac{2 \sqrt{3}}{1}$ by $\frac{3}{3}$ .

$\frac{2 \sqrt{3}}{1} \cdot \frac{3}{3} - \frac{10 \sqrt{3}}{3} + \sqrt{3}$

Step 2.3

Multiply $\frac{2 \sqrt{3}}{1}$ by $\frac{3}{3}$ .

$\frac{2 \sqrt{3} \cdot 3}{3} - \frac{10 \sqrt{3}}{3} + \sqrt{3}$

Step 2.4

Write $\sqrt{3}$ as a fraction with denominator $1$ .

$\frac{2 \sqrt{3} \cdot 3}{3} - \frac{10 \sqrt{3}}{3} + \frac{\sqrt{3}}{1}$

Step 2.5

Multiply $\frac{\sqrt{3}}{1}$ by $\frac{3}{3}$ .

$\frac{2 \sqrt{3} \cdot 3}{3} - \frac{10 \sqrt{3}}{3} + \frac{\sqrt{3}}{1} \cdot \frac{3}{3}$

Step 2.6

Multiply $\frac{\sqrt{3}}{1}$ by $\frac{3}{3}$ .

$\frac{2 \sqrt{3} \cdot 3}{3} - \frac{10 \sqrt{3}}{3} + \frac{\sqrt{3} \cdot 3}{3}$

Step 3

Combine the numerators over the common denominator.

$\frac{2 \sqrt{3} \cdot 3 - 10 \sqrt{3} + \sqrt{3} \cdot 3}{3}$

Step 4

Simplify each term.

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Step 4.1

Multiply $3$ by $2$ .

$\frac{6 \sqrt{3} - 10 \sqrt{3} + \sqrt{3} \cdot 3}{3}$

Step 4.2

Move $3$ to the left of $\sqrt{3}$ .

$\frac{6 \sqrt{3} - 10 \sqrt{3} + 3 \sqrt{3}}{3}$

Step 5

Simplify by adding terms.

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Step 5.1

Subtract $10 \sqrt{3}$ from $6 \sqrt{3}$ .

$\frac{- 4 \sqrt{3} + 3 \sqrt{3}}{3}$

Step 5.2

Add $- 4 \sqrt{3}$ and $3 \sqrt{3}$ .

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

Step 5.3

Move the negative in front of the fraction.

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

Step 6

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$- 0.57735026 \dots$