Evaluate (-15- square root of -18)/33

$\frac{- 15 - \sqrt{- 18}}{33}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 18$ as $- 1 (18)$ .

$\frac{- 15 - \sqrt{- 1 (18)}}{33}$

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$\frac{- 15 - (\sqrt{- 1} \cdot \sqrt{18})}{33}$

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

$\frac{- 15 - (i \cdot \sqrt{18})}{33}$

Step 2

Simplify the numerator.

Rewrite $18$ as $3^{2} \cdot 2$ .

Factor $9$ out of $18$ .

$\frac{- 15 - i \cdot \sqrt{9 (2)}}{33}$

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

$\frac{- 15 - i \cdot \sqrt{3^{2} \cdot 2}}{33}$

Pull terms out from under the radical.

$\frac{- 15 - i \cdot (3 \sqrt{2})}{33}$

Multiply $3$ by $- 1$ .

$\frac{- 15 - 3 i \sqrt{2}}{33}$

Step 3

Simplify terms.

Cancel the common factor of $- 15 - 3 i \sqrt{2}$ and $33$ .

Factor $3$ out of $- 15$ .

$\frac{3 (- 5) - 3 i \sqrt{2}}{33}$

Factor $3$ out of $- 3 i \sqrt{2}$ .

$\frac{3 (- 5) + 3 (- i \sqrt{2})}{33}$

Factor $3$ out of $3 (- 5) + 3 (- i \sqrt{2})$ .

$\frac{3 (- 5 - i \sqrt{2})}{33}$

Cancel the common factors.

Factor $3$ out of $33$ .

$\frac{3 (- 5 - i \sqrt{2})}{3 \cdot 11}$

Cancel the common factor.

$\frac{3 (- 5 - i \sqrt{2})}{3 \cdot 11}$

Rewrite the expression.

$\frac{- 5 - i \sqrt{2}}{11}$

Rewrite $- 5$ as $- 1 (5)$ .

$\frac{- 1 (5) - i \sqrt{2}}{11}$

Factor $- 1$ out of $- i \sqrt{2}$ .

$\frac{- 1 (5) - (i \sqrt{2})}{11}$

Factor $- 1$ out of $- 1 (5) - (i \sqrt{2})$ .

$\frac{- 1 (5 + i \sqrt{2})}{11}$

Move the negative in front of the fraction.

$- \frac{5 + i \sqrt{2}}{11}$