Evaluate ( square root of -50)/( square root of 2)

$\frac{\sqrt{- 50}}{\sqrt{2}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 50$ as $- 1 (50)$ .

$\frac{\sqrt{- 1 (50)}}{\sqrt{2}}$

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{50}}{\sqrt{2}}$

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

$\frac{i \cdot \sqrt{50}}{\sqrt{2}}$

Step 2

Combine $\sqrt{50}$ and $\sqrt{2}$ into a single radical.

$i \cdot \sqrt{\frac{50}{2}}$

Step 3

Simplify the expression.

Divide $50$ by $2$ .

$i \cdot \sqrt{25}$

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 $i$ .

$5 i$