Finite Math Examples

$\frac{\sqrt{- 448}}{- 64}$

Step 1

Pull out imaginary unit $i$ .

Tap for more steps...

Step 1.1

Rewrite $- 448$ as $- 1 (448)$ .

$\frac{\sqrt{- 1 (448)}}{- 64}$

Step 1.2

Rewrite $\sqrt{- 1 (448)}$ as $\sqrt{- 1} \cdot \sqrt{448}$ .

$\frac{\sqrt{- 1} \cdot \sqrt{448}}{- 64}$

Step 1.3

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

$\frac{i \cdot \sqrt{448}}{- 64}$

Step 2

Simplify the numerator.

Tap for more steps...

Step 2.1

Rewrite $448$ as $8^{2} \cdot 7$ .

Tap for more steps...

Step 2.1.1

Factor $64$ out of $448$ .

$\frac{i \sqrt{64 (7)}}{- 64}$

Step 2.1.2

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

$\frac{i \sqrt{8^{2} \cdot 7}}{- 64}$

Step 2.2

Pull terms out from under the radical.

$\frac{i \cdot 8 \sqrt{7}}{- 64}$

Step 3

Reduce the expression by cancelling the common factors.

Tap for more steps...

Step 3.1

Move $8$ to the left of $i$ .

$\frac{8 i \sqrt{7}}{- 64}$

Step 3.2

Cancel the common factor of $8$ and $- 64$ .

Tap for more steps...

Step 3.2.1

Factor $8$ out of $8 i \sqrt{7}$ .

$\frac{8 (i \sqrt{7})}{- 64}$

Step 3.2.2

Cancel the common factors.

Tap for more steps...

Step 3.2.2.1

Factor $8$ out of $- 64$ .

$\frac{8 (i \sqrt{7})}{8 \cdot - 8}$

Step 3.2.2.2

Cancel the common factor.

$\frac{8 (i \sqrt{7})}{8 \cdot - 8}$

Step 3.2.2.3

Rewrite the expression.

$\frac{i \sqrt{7}}{- 8}$

Step 3.3

Move the negative in front of the fraction.

$- \frac{i \sqrt{7}}{8}$