Finite Math Examples

$\frac{- 20 + \sqrt{- 45}}{24}$

Step 1

Rewrite $- 45$ as $- 1 (45)$ .

$\frac{- 20 + \sqrt{- 1 (45)}}{24}$

Step 2

Rewrite $\sqrt{- 1 (45)}$ as $\sqrt{- 1} \cdot \sqrt{45}$ .

$\frac{- 20 + \sqrt{- 1} \cdot \sqrt{45}}{24}$

Step 3

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

$\frac{- 20 + i \cdot \sqrt{45}}{24}$

Step 4

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 4.1

Factor $9$ out of $45$ .

$\frac{- 20 + i \cdot \sqrt{9 (5)}}{24}$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$\frac{- 20 + i \cdot \sqrt{3^{2} \cdot 5}}{24}$

Step 5

Pull terms out from under the radical.

$\frac{- 20 + i (3 \sqrt{5})}{24}$

Step 6

Remove parentheses.

$\frac{- 20 + i \cdot 3 \sqrt{5}}{24}$

Step 7

Move $3$ to the left of $i$ .

$\frac{- 20 + 3 i \sqrt{5}}{24}$