Simplify 20 square root of -1/100-12 square root of -1/16

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

Step 1

Simplify each term.

Move the negative in front of the fraction.

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

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

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

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

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

Cancel the common factor of $10$ .

Factor $10$ out of $20$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

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

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

Cancel the common factor of $4$ .

Factor $4$ out of $- 12$ .

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

Cancel the common factor.

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

Rewrite the expression.

$2 i - 3 i$

Step 2

Subtract $3 i$ from $2 i$ .

$- i$