Algebra Examples

$- \frac{2}{3} \sqrt{- 9}$

Step 1

Rewrite $- 9$ as $- 1 (9)$ .

$- \frac{2}{3} \cdot \sqrt{- 1 (9)}$

Step 2

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$- \frac{2}{3} \cdot (\sqrt{- 1} \cdot \sqrt{9})$

Step 3

Rewrite $\sqrt{- 1}$ as $i$ .

$- \frac{2}{3} \cdot (i \cdot \sqrt{9})$

Step 4

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

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

Step 5

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

$- \frac{2}{3} \cdot (i \cdot 3)$

Step 6

Cancel the common factor of $3$ .

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Step 6.1

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} \cdot (i \cdot 3)$

Step 6.2

Factor $3$ out of $i \cdot 3$ .

$\frac{- 2}{3} \cdot (3 \cdot i)$

Step 6.3

Cancel the common factor.

$\frac{- 2}{3} \cdot (3 \cdot i)$

Step 6.4

Rewrite the expression.

$- 2 \cdot i$

$- 2 i$