Simplify 2+ square root of -25

$2 + \sqrt{- 25}$

Step 1

Rewrite $- 25$ as $- 1 (25)$ .

$2 + \sqrt{- 1 (25)}$

Step 2

Rewrite $\sqrt{- 1 (25)}$ as $\sqrt{- 1} \cdot \sqrt{25}$ .

$2 + \sqrt{- 1} \cdot \sqrt{25}$

Step 3

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

$2 + i \cdot \sqrt{25}$

Step 4

Rewrite $25$ as $5^{2}$ .

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

Step 5

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

$2 + i \cdot 5$

Step 6

Move $5$ to the left of $i$ .

$2 + 5 i$