Algebra Examples

$20 \sqrt{\frac{- 1}{100}} - 12 \sqrt{- \frac{1}{16}}$

Step 1

Simplify each term.

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Step 1.1

Move the negative in front of the fraction.

$20 \sqrt{- \frac{1}{100}} - 12 \sqrt{- \frac{1}{16}}$

Step 1.2

Rewrite $- \frac{1}{100}$ as ${(\frac{i}{10})}^{2}$ .

$20 \sqrt{{(\frac{i}{10})}^{2}} - 12 \sqrt{- \frac{1}{16}}$

Step 1.3

Pull terms out from under the radical, assuming positive real numbers.

$20 \frac{i}{10} - 12 \sqrt{- \frac{1}{16}}$

Step 1.4

Cancel the common factor of $10$ .

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Step 1.4.1

Factor $10$ out of $20$ .

$10 (2) \frac{i}{10} - 12 \sqrt{- \frac{1}{16}}$

Step 1.4.2

Cancel the common factor.

$10 \cdot 2 \frac{i}{10} - 12 \sqrt{- \frac{1}{16}}$

Step 1.4.3

Rewrite the expression.

$2 i - 12 \sqrt{- \frac{1}{16}}$

Step 1.5

Rewrite $- \frac{1}{16}$ as ${(\frac{i}{4})}^{2}$ .

$2 i - 12 \sqrt{{(\frac{i}{4})}^{2}}$

Step 1.6

Pull terms out from under the radical, assuming positive real numbers.

$2 i - 12 \frac{i}{4}$

Step 1.7

Cancel the common factor of $4$ .

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Step 1.7.1

Factor $4$ out of $- 12$ .

$2 i + 4 (- 3) \frac{i}{4}$

Step 1.7.2

Cancel the common factor.

$2 i + 4 \cdot - 3 \frac{i}{4}$

Step 1.7.3

Rewrite the expression.

$2 i - 3 i$

Step 2

Subtract $3 i$ from $2 i$ .

$- i$