Evaluate ( square root of -75)/( square root of 3)

$\frac{\sqrt{- 75}}{\sqrt{3}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 75$ as $- 1 (75)$ .

$\frac{\sqrt{- 1 (75)}}{\sqrt{3}}$

Rewrite $\sqrt{- 1 (75)}$ as $\sqrt{- 1} \cdot \sqrt{75}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{75}}{\sqrt{3}}$

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

$\frac{i \cdot \sqrt{75}}{\sqrt{3}}$

Step 2

Combine $\sqrt{75}$ and $\sqrt{3}$ into a single radical.

$i \cdot \sqrt{\frac{75}{3}}$

Step 3

Simplify the expression.

Divide $75$ by $3$ .

$i \cdot \sqrt{25}$

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 $i$ .

$5 i$