Simplify (8- square root of -20)/4

$\frac{8 - \sqrt{- 20}}{4}$

Pull out imaginary unit $i$ .

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Rewrite $- 20$ as $- 1 (20)$ .

$\frac{8 - \sqrt{- 1 (20)}}{4}$

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$\frac{8 - (\sqrt{- 1} \cdot \sqrt{20})}{4}$

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

$\frac{8 - (i \cdot \sqrt{20})}{4}$

Simplify the numerator.

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Rewrite $20$ as $2^{2} \cdot 5$ .

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Factor $4$ out of $20$ .

$\frac{8 - (i \cdot \sqrt{4 (5)})}{4}$

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

$\frac{8 - (i \cdot \sqrt{2^{2} \cdot 5})}{4}$

Pull terms out from under the radical.

$\frac{8 - (i \cdot (2 \sqrt{5}))}{4}$

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

$\frac{8 - (2 \cdot i \sqrt{5})}{4}$

Multiply $2$ by $- 1$ .

$\frac{8 - 2 i \sqrt{5}}{4}$

Cancel the common factor of $8 - 2 i \sqrt{5}$ and $4$ .

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Factor $2$ out of $8$ .

$\frac{2 (4) - 2 i \sqrt{5}}{4}$

Factor $2$ out of $- 2 i \sqrt{5}$ .

$\frac{2 (4) + 2 (- i \sqrt{5})}{4}$

Factor $2$ out of $2 (4) + 2 (- i \sqrt{5})$ .

$\frac{2 (4 - i \sqrt{5})}{4}$

Cancel the common factors.

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Factor $2$ out of $4$ .

$\frac{2 (4 - i \sqrt{5})}{2 \cdot 2}$

Cancel the common factor.

$\frac{2 (4 - i \sqrt{5})}{2 \cdot 2}$

Rewrite the expression.

$\frac{4 - i \sqrt{5}}{2}$

Simplify (8- square root of -20)/4

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