Pre-Algebra Examples

$\sqrt{2} \cdot \sqrt{- 14}$

Step 1

Rewrite $- 14$ as $- 1 (14)$ .

$\sqrt{2} \cdot \sqrt{- 1 (14)}$

Step 2

Rewrite $\sqrt{- 1 (14)}$ as $\sqrt{- 1} \cdot \sqrt{14}$ .

$\sqrt{2} \cdot (\sqrt{- 1} \cdot \sqrt{14})$

Step 3

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

$\sqrt{2} \cdot (i \cdot \sqrt{14})$

Step 4

Multiply $\sqrt{2} (i \sqrt{14})$ .

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Step 4.1

Combine using the product rule for radicals.

$\sqrt{14 \cdot 2} i$

Step 4.2

Multiply $14$ by $2$ .

$\sqrt{28} i$

Step 5

Rewrite $28$ as $2^{2} \cdot 7$ .

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Step 5.1

Factor $4$ out of $28$ .

$\sqrt{4 (7)} i$

Step 5.2

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

$\sqrt{2^{2} \cdot 7} i$

Step 6

Pull terms out from under the radical.

$2 \sqrt{7} i$