Divide ( square root of -18)/( square root of 2)

$\frac{\sqrt{- 18}}{\sqrt{2}}$

Pull out imaginary unit $i$ .

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

$\frac{\sqrt{- 1 (18)}}{\sqrt{2}}$

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

$\frac{\sqrt{- 1} \cdot \sqrt{18}}{\sqrt{2}}$

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

$\frac{i \cdot \sqrt{18}}{\sqrt{2}}$

Combine $\sqrt{18}$ and $\sqrt{2}$ into a single radical.

$i \cdot \sqrt{\frac{18}{2}}$

Divide $18$ by $2$ .

$i \cdot \sqrt{9}$

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

$i \cdot \sqrt{3^{2}}$

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

$i \cdot 3$

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

$3 i$

Divide ( square root of -18)/( square root of 2)

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