Basic Math Examples

$7 \sqrt{6} \cdot (2 \sqrt{- 3})$

Step 1

Rewrite $- 3$ as $- 1 (3)$ .

$7 \sqrt{6} \cdot (2 \sqrt{- 1 (3)})$

Step 2

Rewrite $\sqrt{- 1 (3)}$ as $\sqrt{- 1} \cdot \sqrt{3}$ .

$7 \sqrt{6} \cdot (2 (\sqrt{- 1} \cdot \sqrt{3}))$

Step 3

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

$7 \sqrt{6} \cdot (2 (i \cdot \sqrt{3}))$

Step 4

Multiply $7 \sqrt{6} (2 i \sqrt{3})$ .

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Step 4.1

Multiply $2$ by $7$ .

$14 \sqrt{6} (i \sqrt{3})$

Step 4.2

Combine using the product rule for radicals.

$14 \sqrt{3 \cdot 6} i$

Step 4.3

Multiply $3$ by $6$ .

$14 \sqrt{18} i$

Step 5

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

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Step 5.1

Factor $9$ out of $18$ .

$14 \sqrt{9 (2)} i$

Step 5.2

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

$14 \sqrt{3^{2} \cdot 2} i$

Step 6

Pull terms out from under the radical.

$14 (3 \sqrt{2}) i$

Step 7

Multiply $3$ by $14$ .

$42 \sqrt{2} i$