Evaluate ( square root of -56)/( square root of 7)

$\frac{\sqrt{- 56}}{\sqrt{7}}$

Step 1

Pull out imaginary unit $i$ .

Rewrite $- 56$ as $- 1 (56)$ .

$\frac{\sqrt{- 1 (56)}}{\sqrt{7}}$

Rewrite $\sqrt{- 1 (56)}$ as $\sqrt{- 1} \cdot \sqrt{56}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{56}}{\sqrt{7}}$

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

$\frac{i \cdot \sqrt{56}}{\sqrt{7}}$

Step 2

Combine $\sqrt{56}$ and $\sqrt{7}$ into a single radical.

$i \cdot \sqrt{\frac{56}{7}}$

Step 3

Divide $56$ by $7$ .

$i \cdot \sqrt{8}$

Step 4

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$i \cdot \sqrt{4 (2)}$

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

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

$2 i \sqrt{2}$