Simplify ( square root of 72)/( square root of -18)

$\frac{\sqrt{72}}{\sqrt{- 18}}$

Pull out imaginary unit $i$ .

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

$\frac{\sqrt{72}}{\sqrt{- 1 (18)}}$

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

$\frac{\sqrt{72}}{\sqrt{- 1} \cdot \sqrt{18}}$

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

$\frac{\sqrt{72}}{i \cdot \sqrt{18}}$

Combine $\sqrt{72}$ and $\sqrt{18}$ into a single radical.

$\frac{\sqrt{\frac{72}{18}}}{i}$

Cancel the common factor of $72$ and $18$ .

Factor $18$ out of $72$ .

$\frac{\sqrt{\frac{18 \cdot 4}{18}}}{i}$

Cancel the common factors.

Factor $18$ out of $18$ .

$\frac{\sqrt{\frac{18 \cdot 4}{18 (1)}}}{i}$

Cancel the common factor.

$\frac{\sqrt{\frac{18 \cdot 4}{18 \cdot 1}}}{i}$

Rewrite the expression.

$\frac{\sqrt{\frac{4}{1}}}{i}$

Divide $4$ by $1$ .

$\frac{\sqrt{4}}{i}$

Simplify the numerator.

Rewrite $4$ as $2^{2}$ .

$\frac{\sqrt{2^{2}}}{i}$

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

$\frac{2}{i}$