Precalculus Examples

$\sqrt{- 15} \cdot \sqrt{10}$

Step 1

Rewrite $- 15$ as $- 1 (15)$ .

$\sqrt{- 1 (15)} \cdot \sqrt{10}$

Step 2

Rewrite $\sqrt{- 1 (15)}$ as $\sqrt{- 1} \cdot \sqrt{15}$ .

$\sqrt{- 1} \cdot \sqrt{15} \cdot \sqrt{10}$

Step 3

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

$i \cdot \sqrt{15} \cdot \sqrt{10}$

Step 4

Multiply $i \sqrt{15} \sqrt{10}$ .

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Step 4.1

Combine using the product rule for radicals.

$i \sqrt{10 \cdot 15}$

Step 4.2

Multiply $10$ by $15$ .

$i \sqrt{150}$

Step 5

Rewrite $150$ as $5^{2} \cdot 6$ .

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Step 5.1

Factor $25$ out of $150$ .

$i \sqrt{25 (6)}$

Step 5.2

Rewrite $25$ as $5^{2}$ .

$i \sqrt{5^{2} \cdot 6}$

Step 6

Pull terms out from under the radical.

$i (5 \sqrt{6})$

Step 7

Move $5$ to the left of $i$ .

$5 i \sqrt{6}$