Basic Math Examples

$(\sqrt{3 + 2 i}) (\sqrt{6 - \sqrt{- 8}})$

Step 1

Rewrite $- 8$ as $- 1 (8)$ .

$\sqrt{3 + 2 i} \sqrt{6 - \sqrt{- 1 (8)}}$

Step 2

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$\sqrt{3 + 2 i} \sqrt{6 - (\sqrt{- 1} \cdot \sqrt{8})}$

Step 3

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

$\sqrt{3 + 2 i} \sqrt{6 - (i \cdot \sqrt{8})}$

Step 4

Combine using the product rule for radicals.

$\sqrt{(3 + 2 i) (6 - (i \cdot \sqrt{8}))}$

Step 5

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

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Step 5.1

Factor $4$ out of $8$ .

$\sqrt{(3 + 2 i) (6 - i \cdot \sqrt{4 (2)})}$

Step 5.2

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

$\sqrt{(3 + 2 i) (6 - i \cdot \sqrt{2^{2} \cdot 2})}$

Step 6

Pull terms out from under the radical.

$\sqrt{(3 + 2 i) (6 - i \cdot (2 \sqrt{2}))}$

Step 7

Multiply $2$ by $- 1$ .

$\sqrt{(3 + 2 i) (6 - 2 i \sqrt{2})}$