Simplify ( square root of -120)/( square root of 10)

$\frac{\sqrt{- 120}}{\sqrt{10}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 120$ as $- 1 (120)$ .

$\frac{\sqrt{- 1 (120)}}{\sqrt{10}}$

Rewrite $\sqrt{- 1 (120)}$ as $\sqrt{- 1} \cdot \sqrt{120}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{120}}{\sqrt{10}}$

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

$\frac{i \cdot \sqrt{120}}{\sqrt{10}}$

Step 2

Combine $\sqrt{120}$ and $\sqrt{10}$ into a single radical.

$i \cdot \sqrt{\frac{120}{10}}$

Step 3

Divide $120$ by $10$ .

$i \cdot \sqrt{12}$

Step 4

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$i \cdot \sqrt{4 (3)}$

Rewrite $4$ as $2^{2}$ .

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

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{3})$

Step 6

Move $2$ to the left of $i$ .

$2 i \sqrt{3}$