Precalculus Examples

$\sqrt{- 100 \cdot \sqrt{- 81}}$

Step 1

Rewrite $- 81$ as $- 1 (81)$ .

$\sqrt{- 100 \sqrt{- 1 (81)}}$

Step 2

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$\sqrt{- 100 (\sqrt{- 1} \cdot \sqrt{81})}$

Step 3

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

$\sqrt{- 100 (i \cdot \sqrt{81})}$

Step 4

Rewrite $81$ as $9^{2}$ .

$\sqrt{- 100 (i \cdot \sqrt{9^{2}})}$

Step 5

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

$\sqrt{- 100 (i \cdot 9)}$

Step 6

Move $9$ to the left of $i$ .

$\sqrt{- 100 (9 \cdot i)}$

Step 7

Remove unnecessary parentheses.

$\sqrt{- 100 \cdot 9 i}$

Step 8

Write the expression using exponents.

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Step 8.1

Multiply $- 100$ by $9$ .

$\sqrt{- 900 i}$

Step 8.2

Rewrite $- 900$ as ${(30 i)}^{2}$ .

$\sqrt{{(30 i)}^{2} i}$

Step 9

Pull terms out from under the radical.

$30 i \sqrt{i}$