Simplify ( square root of -125)/( square root of 5)

$\frac{\sqrt{- 125}}{\sqrt{5}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 125$ as $- 1 (125)$ .

$\frac{\sqrt{- 1 (125)}}{\sqrt{5}}$

Rewrite $\sqrt{- 1 (125)}$ as $\sqrt{- 1} \cdot \sqrt{125}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{125}}{\sqrt{5}}$

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

$\frac{i \cdot \sqrt{125}}{\sqrt{5}}$

Step 2

Combine $\sqrt{125}$ and $\sqrt{5}$ into a single radical.

$i \cdot \sqrt{\frac{125}{5}}$

Step 3

Simplify the expression.

Divide $125$ by $5$ .

$i \cdot \sqrt{25}$

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

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

Step 4

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

$i \cdot 5$

Step 5

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

$5 i$