Simplify the Radical Expression square root of -25

$\sqrt{- 25}$

Step 1

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

$\sqrt{- 1 (25)}$

Step 2

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

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

Step 3

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

$i \cdot \sqrt{25}$

Step 4

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

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

Step 5

Pull terms out from under the radical.

$i \cdot | 5 |$

Step 6

The absolute value is the distance between a number and zero. The distance between $0$ and $5$ is $5$ .

$i \cdot 5$

Step 7

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

$5 i$