Algebra Examples

$\frac{1}{8} \sqrt{- 64}$

Step 1

Rewrite $- 64$ as $- 1 (64)$ .

$\frac{1}{8} \cdot \sqrt{- 1 (64)}$

Step 2

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$\frac{1}{8} \cdot (\sqrt{- 1} \cdot \sqrt{64})$

Step 3

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

$\frac{1}{8} \cdot (i \cdot \sqrt{64})$

Step 4

Simplify the expression.

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Step 4.1

Rewrite $64$ as $8^{2}$ .

$\frac{1}{8} \cdot (i \cdot \sqrt{8^{2}})$

Step 4.2

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

$\frac{1}{8} \cdot (i \cdot 8)$

Step 5

Cancel the common factor of $8$ .

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Step 5.1

Factor $8$ out of $i \cdot 8$ .

$\frac{1}{8} \cdot (8 \cdot i)$

Step 5.2

Cancel the common factor.

$\frac{1}{8} \cdot (8 \cdot i)$

Step 5.3

Rewrite the expression.

$i$