Basic Math Examples

$\sqrt{15} \cdot \sqrt{- 3}$

Step 1

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

$\sqrt{15} \cdot \sqrt{- 1 (3)}$

Step 2

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

$\sqrt{15} \cdot (\sqrt{- 1} \cdot \sqrt{3})$

Step 3

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

$\sqrt{15} \cdot (i \cdot \sqrt{3})$

Step 4

Multiply $\sqrt{15} (i \sqrt{3})$ .

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Step 4.1

Combine using the product rule for radicals.

$\sqrt{3 \cdot 15} i$

Step 4.2

Multiply $3$ by $15$ .

$\sqrt{45} i$

Step 5

Rewrite $45$ as $3^{2} \cdot 5$ .

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Step 5.1

Factor $9$ out of $45$ .

$\sqrt{9 (5)} i$

Step 5.2

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

$\sqrt{3^{2} \cdot 5} i$

Step 6

Pull terms out from under the radical.

$3 \sqrt{5} i$