Pre-Algebra Examples

$\sqrt{- 18} (\sqrt{- 3 - \sqrt{7}})$

Step 1

Rewrite $- 18$ as $- 1 (18)$ .

$\sqrt{- 1 (18)} \sqrt{- 3 - \sqrt{7}}$

Step 2

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$\sqrt{- 1} \cdot \sqrt{18} \sqrt{- 3 - \sqrt{7}}$

Step 3

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

$i \cdot \sqrt{18} \sqrt{- 3 - \sqrt{7}}$

Step 4

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 4.1

Factor $9$ out of $18$ .

$i \cdot \sqrt{9 (2)} \sqrt{- 3 - \sqrt{7}}$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$i \cdot \sqrt{3^{2} \cdot 2} \sqrt{- 3 - \sqrt{7}}$

Step 5

Pull terms out from under the radical.

$i \cdot (3 \sqrt{2}) \sqrt{- 3 - \sqrt{7}}$

Step 6

Move $3$ to the left of $i$ .

$3 \cdot i \sqrt{2} \sqrt{- 3 - \sqrt{7}}$

Step 7

Combine using the product rule for radicals.

$3 i \sqrt{(- 3 - \sqrt{7}) \cdot 2}$