Evaluate square root of -32- square root of -18

$\sqrt{- 32} - \sqrt{- 18}$

Step 1

Simplify each term.

Rewrite $- 32$ as $- 1 (32)$ .

$\sqrt{- 1 (32)} - \sqrt{- 18}$

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$\sqrt{- 1} \cdot \sqrt{32} - \sqrt{- 18}$

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

$i \cdot \sqrt{32} - \sqrt{- 18}$

Rewrite $32$ as $4^{2} \cdot 2$ .

Factor $16$ out of $32$ .

$i \cdot \sqrt{16 (2)} - \sqrt{- 18}$

Rewrite $16$ as $4^{2}$ .

$i \cdot \sqrt{4^{2} \cdot 2} - \sqrt{- 18}$

Pull terms out from under the radical.

$i \cdot (4 \sqrt{2}) - \sqrt{- 18}$

Move $4$ to the left of $i$ .

$4 \cdot i \sqrt{2} - \sqrt{- 18}$

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

$4 i \sqrt{2} - \sqrt{- 1 (18)}$

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

$4 i \sqrt{2} - (\sqrt{- 1} \cdot \sqrt{18})$

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

$4 i \sqrt{2} - (i \cdot \sqrt{18})$

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

Factor $9$ out of $18$ .

$4 i \sqrt{2} - (i \cdot \sqrt{9 (2)})$

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

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

Pull terms out from under the radical.

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

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

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

Multiply $3$ by $- 1$ .

$4 i \sqrt{2} - 3 i \sqrt{2}$

Step 2

Simplify by adding terms.

Subtract $3 i \sqrt{2}$ from $4 i \sqrt{2}$ .

$1 i \sqrt{2}$

Multiply $i$ by $1$ .

$i \sqrt{2}$