Algebra Examples

$\sqrt{- 36} - \sqrt{- 32}$

Step 1

Rewrite $- 36$ as $- 1 (36)$ .

$\sqrt{- 1 (36)} - \sqrt{- 32}$

Step 2

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$\sqrt{- 1} \cdot \sqrt{36} - \sqrt{- 32}$

Step 3

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

$i \cdot \sqrt{36} - \sqrt{- 32}$

Step 4

Rewrite $36$ as $6^{2}$ .

$i \cdot \sqrt{6^{2}} - \sqrt{- 32}$

Step 5

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

$i \cdot 6 - \sqrt{- 32}$

Step 6

Move $6$ to the left of $i$ .

$6 \cdot i - \sqrt{- 32}$

Step 7

Rewrite $- 32$ as $- 1 (32)$ .

$6 i - \sqrt{- 1 (32)}$

Step 8

Rewrite $\sqrt{- 1 (32)}$ as $\sqrt{- 1} \cdot \sqrt{32}$ .

$6 i - (\sqrt{- 1} \cdot \sqrt{32})$

Step 9

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

$6 i - (i \cdot \sqrt{32})$

Step 10

Rewrite $32$ as $4^{2} \cdot 2$ .

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Step 10.1

Factor $16$ out of $32$ .

$6 i - (i \cdot \sqrt{16 (2)})$

Step 10.2

Rewrite $16$ as $4^{2}$ .

$6 i - (i \cdot \sqrt{4^{2} \cdot 2})$

Step 11

Pull terms out from under the radical.

$6 i - (i \cdot (4 \sqrt{2}))$

Step 12

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

$6 i - (4 \cdot i \sqrt{2})$

Step 13

Multiply $4$ by $- 1$ .

$6 i - 4 i \sqrt{2}$