Precalculus Examples

$\sqrt{\frac{1}{4}} \sqrt{- 64}$

Step 1

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

$\sqrt{\frac{1}{4}} \sqrt{- 1 (64)}$

Step 2

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

$\sqrt{\frac{1}{4}} (\sqrt{- 1} \cdot \sqrt{64})$

Step 3

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

$\sqrt{\frac{1}{4}} (i \cdot \sqrt{64})$

Step 4

Rewrite $\sqrt{\frac{1}{4}}$ as $\frac{\sqrt{1}}{\sqrt{4}}$ .

$\frac{\sqrt{1}}{\sqrt{4}} (i \cdot \sqrt{64})$

Step 5

Any root of $1$ is $1$ .

$\frac{1}{\sqrt{4}} (i \cdot \sqrt{64})$

Step 6

Simplify the denominator.

Tap for more steps...

Step 6.1

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

$\frac{1}{\sqrt{2^{2}}} (i \cdot \sqrt{64})$

Step 6.2

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

$\frac{1}{2} (i \cdot \sqrt{64})$

Step 7

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 7.1

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

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

Step 7.2

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

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

Step 7.3

Cancel the common factor of $2$ .

Tap for more steps...

Step 7.3.1

Factor $2$ out of $i \cdot 8$ .

$\frac{1}{2} (2 (i \cdot 4))$

Step 7.3.2

Cancel the common factor.

$\frac{1}{2} (2 (i \cdot 4))$

Step 7.3.3

Rewrite the expression.

$i \cdot 4$

Step 7.4

Move $4$ to the left of $i$ .

$4 i$