Finite Math Examples

$\sqrt{- 128} + \sqrt{- 95}$

Step 1

Rewrite $- 128$ as $- 1 (128)$ .

$\sqrt{- 1 (128)} + \sqrt{- 95}$

Step 2

Rewrite $\sqrt{- 1 (128)}$ as $\sqrt{- 1} \cdot \sqrt{128}$ .

$\sqrt{- 1} \cdot \sqrt{128} + \sqrt{- 95}$

Step 3

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

$i \cdot \sqrt{128} + \sqrt{- 95}$

Step 4

Rewrite $128$ as $8^{2} \cdot 2$ .

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Step 4.1

Factor $64$ out of $128$ .

$i \cdot \sqrt{64 (2)} + \sqrt{- 95}$

Step 4.2

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

$i \cdot \sqrt{8^{2} \cdot 2} + \sqrt{- 95}$

Step 5

Pull terms out from under the radical.

$i \cdot (8 \sqrt{2}) + \sqrt{- 95}$

Step 6

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

$8 \cdot i \sqrt{2} + \sqrt{- 95}$

Step 7

Rewrite $- 95$ as $- 1 (95)$ .

$8 i \sqrt{2} + \sqrt{- 1 (95)}$

Step 8

Rewrite $\sqrt{- 1 (95)}$ as $\sqrt{- 1} \cdot \sqrt{95}$ .

$8 i \sqrt{2} + \sqrt{- 1} \cdot \sqrt{95}$

Step 9

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

$8 i \sqrt{2} + i \sqrt{95}$