Finite Math Examples

$\sqrt{- 196} - \sqrt{- 256}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 196$ as $- 1 (196)$ .

$\sqrt{- 1 (196)} - \sqrt{- 256}$

Step 1.2

Rewrite $\sqrt{- 1 (196)}$ as $\sqrt{- 1} \cdot \sqrt{196}$ .

$\sqrt{- 1} \cdot \sqrt{196} - \sqrt{- 256}$

Step 1.3

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

$i \cdot \sqrt{196} - \sqrt{- 256}$

Step 1.4

Rewrite $196$ as $14^{2}$ .

$i \cdot \sqrt{14^{2}} - \sqrt{- 256}$

Step 1.5

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

$i \cdot 14 - \sqrt{- 256}$

Step 1.6

Move $14$ to the left of $i$ .

$14 \cdot i - \sqrt{- 256}$

Step 1.7

Rewrite $- 256$ as $- 1 (256)$ .

$14 i - \sqrt{- 1 (256)}$

Step 1.8

Rewrite $\sqrt{- 1 (256)}$ as $\sqrt{- 1} \cdot \sqrt{256}$ .

$14 i - (\sqrt{- 1} \cdot \sqrt{256})$

Step 1.9

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

$14 i - (i \cdot \sqrt{256})$

Step 1.10

Rewrite $256$ as $16^{2}$ .

$14 i - (i \cdot \sqrt{16^{2}})$

Step 1.11

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

$14 i - (i \cdot 16)$

Step 1.12

Move $16$ to the left of $i$ .

$14 i - (16 \cdot i)$

Step 1.13

Multiply $16$ by $- 1$ .

$14 i - 16 i$

Step 2

Subtract $16 i$ from $14 i$ .

$- 2 i$