Evaluate square root of -153

$\sqrt{- 153}$

Step 1

Rewrite $- 153$ as $- 1 (153)$ .

$\sqrt{- 1 (153)}$

Step 2

Rewrite $\sqrt{- 1 (153)}$ as $\sqrt{- 1} \cdot \sqrt{153}$ .

$\sqrt{- 1} \cdot \sqrt{153}$

Step 3

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

$i \cdot \sqrt{153}$

Step 4

Rewrite $153$ as $3^{2} \cdot 17$ .

Factor $9$ out of $153$ .

$i \cdot \sqrt{9 (17)}$

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

$i \cdot \sqrt{3^{2} \cdot 17}$

Step 5

Pull terms out from under the radical.

$i \cdot (3 \sqrt{17})$

Step 6

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

$3 i \sqrt{17}$