Evaluate square root of 9-(-1)^2

$\sqrt{9 - {(- 1)}^{2}}$

Step 1

Multiply $- 1$ by ${(- 1)}^{2}$ by adding the exponents.

Multiply $- 1$ by ${(- 1)}^{2}$ .

Raise $- 1$ to the power of $1$ .

$\sqrt{9 + {(- 1)}^{1} {(- 1)}^{2}}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{9 + {(- 1)}^{1 + 2}}$

Add $1$ and $2$ .

$\sqrt{9 + {(- 1)}^{3}}$

Step 2

Raise $- 1$ to the power of $3$ .

$\sqrt{9 - 1}$

Step 3

Subtract $1$ from $9$ .

$\sqrt{8}$

Step 4

Rewrite $8$ as $2^{2} \cdot 2$ .

Factor $4$ out of $8$ .

$\sqrt{4 (2)}$

Rewrite $4$ as $2^{2}$ .

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

Step 5

Pull terms out from under the radical.

$2 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$2 \sqrt{2}$

Decimal Form:

$2.82842712 \dots$