Algebra Examples

$\sqrt{- {(- 9)}^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Raise $- 9$ to the power of $2$ .

$\sqrt{- 1 \cdot 81}$

Step 1.2

Multiply $- 1$ by $81$ .

$\sqrt{- 81}$

Step 2

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

$\sqrt{- 1 (81)}$

Step 3

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

$\sqrt{- 1} \cdot \sqrt{81}$

Step 4

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

$i \cdot \sqrt{81}$

Step 5

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

$i \cdot \sqrt{9^{2}}$

Step 6

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

$i \cdot 9$

Step 7

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

$9 i$