Linear Algebra Examples

$\sqrt{{(3 - 2)}^{2} + (- 1 - {(- 3)}^{2})}$

Step 1

Simplify the expression.

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Step 1.1

Remove parentheses.

$\sqrt{{(3 - 2)}^{2} - 1 - {(- 3)}^{2}}$

Step 1.2

Subtract $2$ from $3$ .

$\sqrt{1^{2} - 1 - {(- 3)}^{2}}$

Step 1.3

One to any power is one.

$\sqrt{1 - 1 - {(- 3)}^{2}}$

Step 1.4

Raise $- 3$ to the power of $2$ .

$\sqrt{1 - 1 - 1 \cdot 9}$

Step 1.5

Multiply $- 1$ by $9$ .

$\sqrt{1 - 1 - 9}$

Step 1.6

Subtract $1$ from $1$ .

$\sqrt{0 - 9}$

Step 1.7

Subtract $9$ from $0$ .

$\sqrt{- 9}$

Step 2

Rewrite $- 9$ as $- 1 (9)$ .

$\sqrt{- 1 (9)}$

Step 3

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$\sqrt{- 1} \cdot \sqrt{9}$

Step 4

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

$i \cdot \sqrt{9}$

Step 5

Rewrite $9$ as $3^{2}$ .

$i \cdot \sqrt{3^{2}}$

Step 6

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

$i \cdot 3$

Step 7

Move $3$ to the left of $i$ .

$3 i$