Algebra Examples

$\sqrt{12} - \frac{2}{5} \cdot \sqrt{75}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $4$ out of $12$ .

$\sqrt{4 (3)} - \frac{2}{5} \cdot \sqrt{75}$

Step 1.1.2

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

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

Step 1.2

Pull terms out from under the radical.

$2 \sqrt{3} - \frac{2}{5} \cdot \sqrt{75}$

Step 1.3

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

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Step 1.3.1

Factor $25$ out of $75$ .

$2 \sqrt{3} - \frac{2}{5} \cdot \sqrt{25 (3)}$

Step 1.3.2

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

$2 \sqrt{3} - \frac{2}{5} \cdot \sqrt{5^{2} \cdot 3}$

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Cancel the common factor of $5$ .

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Step 1.5.1

Move the leading negative in $- \frac{2}{5}$ into the numerator.

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

Step 1.5.2

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

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

Step 1.5.3

Cancel the common factor.

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

Step 1.5.4

Rewrite the expression.

$2 \sqrt{3} - 2 \cdot \sqrt{3}$

$2 \sqrt{3} - 2 \sqrt{3}$

Step 2

Subtract $2 \sqrt{3}$ from $2 \sqrt{3}$ .

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