Simplify the Radical Expression ( 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 $i$ .

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

Rewrite $- 7$ as $- 1 (7)$ .

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

Rewrite $\sqrt{- 1 (7)}$ as $\sqrt{- 1} \cdot \sqrt{7}$ .

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

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

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

Step 2

Cancel the common factor of $i$ .

Cancel the common factor.

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

Rewrite the expression.

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

Step 3

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

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

Step 4

Divide $56$ by $7$ .

$\sqrt{8}$

Step 5

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

Factor $4$ out of $8$ .

$\sqrt{4 (2)}$

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

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

Step 6

Pull terms out from under the radical.

$| 2 | \sqrt{2}$

Step 7

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

$2 \sqrt{2}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$