Simplify square root of -18- square root of -8

$\sqrt{- 18} - \sqrt{- 8}$

Simplify each term.

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

$\sqrt{- 1 (18)} - \sqrt{- 8}$

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

$\sqrt{- 1} \cdot \sqrt{18} - \sqrt{- 8}$

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

$i \cdot \sqrt{18} - \sqrt{- 8}$

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

Factor $9$ out of $18$ .

$i \cdot \sqrt{9 (2)} - \sqrt{- 8}$

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

$i \cdot \sqrt{3^{2} \cdot 2} - \sqrt{- 8}$

Pull terms out from under the radical.

$i \cdot (3 \sqrt{2}) - \sqrt{- 8}$

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

$3 \cdot i \sqrt{2} - \sqrt{- 8}$

Rewrite $- 8$ as $- 1 (8)$ .

$3 i \sqrt{2} - \sqrt{- 1 (8)}$

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$3 i \sqrt{2} - (\sqrt{- 1} \cdot \sqrt{8})$

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

$3 i \sqrt{2} - (i \cdot \sqrt{8})$

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

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

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

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

Pull terms out from under the radical.

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

Move $2$ to the left of $i$ .

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

Multiply $2$ by $- 1$ .

$3 i \sqrt{2} - 2 i \sqrt{2}$

Simplify by adding terms.

Subtract $2 i \sqrt{2}$ from $3 i \sqrt{2}$ .

$1 i \sqrt{2}$

Multiply $i$ by $1$ .

$i \sqrt{2}$