Evaluate square root of -245

$\sqrt{- 245}$

Step 1

Rewrite $- 245$ as $- 1 (245)$ .

$\sqrt{- 1 (245)}$

Step 2

Rewrite $\sqrt{- 1 (245)}$ as $\sqrt{- 1} \cdot \sqrt{245}$ .

$\sqrt{- 1} \cdot \sqrt{245}$

Step 3

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

$i \cdot \sqrt{245}$

Step 4

Rewrite $245$ as $7^{2} \cdot 5$ .

Factor $49$ out of $245$ .

$i \cdot \sqrt{49 (5)}$

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

$i \cdot \sqrt{7^{2} \cdot 5}$

Step 5

Pull terms out from under the radical.

$i \cdot (7 \sqrt{5})$

Step 6

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

$7 i \sqrt{5}$