Algebra Examples

$(\sqrt{- 100}) (\sqrt{36})$

Step 1

Rewrite $- 100$ as $- 1 (100)$ .

$\sqrt{- 1 (100)} \sqrt{36}$

Step 2

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$\sqrt{- 1} \cdot \sqrt{100} \sqrt{36}$

Step 3

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

$i \cdot \sqrt{100} \sqrt{36}$

Step 4

Rewrite $100$ as $10^{2}$ .

$i \cdot \sqrt{10^{2}} \sqrt{36}$

Step 5

Pull terms out from under the radical, assuming positive real numbers.

$i \cdot 10 \sqrt{36}$

Step 6

Move $10$ to the left of $i$ .

$10 \cdot i \sqrt{36}$

Step 7

Rewrite $36$ as $6^{2}$ .

$10 i \sqrt{6^{2}}$

Step 8

Multiply.

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Step 8.1

Pull terms out from under the radical, assuming positive real numbers.

$10 i \cdot 6$

Step 8.2

Multiply $6$ by $10$ .

$60 i$