Simplify square root of -98

$\sqrt{- 98}$

Step 1

Rewrite $- 98$ as $- 1 (98)$ .

$\sqrt{- 1 (98)}$

Step 2

Rewrite $\sqrt{- 1 (98)}$ as $\sqrt{- 1} \cdot \sqrt{98}$ .

$\sqrt{- 1} \cdot \sqrt{98}$

Step 3

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

$i \cdot \sqrt{98}$

Step 4

Rewrite $98$ as $7^{2} \cdot 2$ .

Factor $49$ out of $98$ .

$i \cdot \sqrt{49 (2)}$

Rewrite $49$ as $7^{2}$ .

$i \cdot \sqrt{7^{2} \cdot 2}$

Step 5

Pull terms out from under the radical.

$i \cdot (7 \sqrt{2})$

Step 6

Move $7$ to the left of $i$ .

$7 i \sqrt{2}$