Simplify (-12+ square root of -18)/60

$\frac{- 12 + \sqrt{- 18}}{60}$

Step 1

Pull out imaginary unit $i$ .

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

$\frac{- 12 + \sqrt{- 1 (18)}}{60}$

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

$\frac{- 12 + \sqrt{- 1} \cdot \sqrt{18}}{60}$

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

$\frac{- 12 + i \cdot \sqrt{18}}{60}$

Step 2

Simplify the numerator.

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

Factor $9$ out of $18$ .

$\frac{- 12 + i \cdot \sqrt{9 (2)}}{60}$

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

$\frac{- 12 + i \cdot \sqrt{3^{2} \cdot 2}}{60}$

Pull terms out from under the radical.

$\frac{- 12 + i \cdot (3 \sqrt{2})}{60}$

Move $3$ to the left of $i$ .

$\frac{- 12 + 3 i \sqrt{2}}{60}$

Step 3

Simplify terms.

Cancel the common factor of $- 12 + 3 i \sqrt{2}$ and $60$ .

Factor $3$ out of $- 12$ .

$\frac{3 \cdot - 4 + 3 i \sqrt{2}}{60}$

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

$\frac{3 \cdot - 4 + 3 (i \sqrt{2})}{60}$

Factor $3$ out of $3 \cdot - 4 + 3 (i \sqrt{2})$ .

$\frac{3 \cdot (- 4 + i \sqrt{2})}{60}$

Cancel the common factors.

Factor $3$ out of $60$ .

$\frac{3 \cdot (- 4 + i \sqrt{2})}{3 (20)}$

Cancel the common factor.

$\frac{3 \cdot (- 4 + i \sqrt{2})}{3 \cdot 20}$

Rewrite the expression.

$\frac{- 4 + i \sqrt{2}}{20}$

Rewrite $- 4$ as $- 1 (4)$ .

$\frac{- 1 (4) + i \sqrt{2}}{20}$

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

$\frac{- 1 (4) - (- i \sqrt{2})}{20}$

Factor $- 1$ out of $- 1 (4) - (- i \sqrt{2})$ .

$\frac{- 1 (4 - i \sqrt{2})}{20}$

Move the negative in front of the fraction.

$- \frac{4 - i \sqrt{2}}{20}$