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Evaluate square root of -16/4

$\sqrt{- \frac{16}{4}}$

Step 1

Simplify the expression.

Divide $16$ by $4$ .

$\sqrt{- 1 \cdot 4}$

Multiply $- 1$ by $4$ .

$\sqrt{- 4}$

$\sqrt{- 4}$

Step 2

Rewrite $- 4$ as $- 1 (4)$ .

$\sqrt{- 1 (4)}$

Step 3

Rewrite $\sqrt{- 1 (4)}$ as $\sqrt{- 1} \cdot \sqrt{4}$ .

$\sqrt{- 1} \cdot \sqrt{4}$

Step 4

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

$i \cdot \sqrt{4}$

Step 5

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

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

Step 6

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

$i \cdot 2$

Step 7

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

$2 i$

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