Linear Algebra Examples

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

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

Step 1

Simplify the expression.

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Step 1.1

Remove parentheses.

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

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

Step 1.2

Subtract

2

$2$ from

3

$3$ .

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

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

Step 1.3

One to any power is one.

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

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

Step 1.4

Raise

- 3

$- 3$ to the power of

2

$2$ .

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

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

Step 1.5

Multiply

- 1

$- 1$ by

9

$9$ .

\sqrt{1 - 1 - 9}

$\sqrt{1 - 1 - 9}$

Step 1.6

Subtract

1

$1$ from

1

$1$ .

\sqrt{0 - 9}

$\sqrt{0 - 9}$

Step 1.7

Subtract

9

$9$ from

0

$0$ .

\sqrt{- 9}

$\sqrt{- 9}$

\sqrt{- 9}

$\sqrt{- 9}$

Step 2

Rewrite

- 9

$- 9$ as

- 1 (9)

$- 1 (9)$ .

\sqrt{- 1 (9)}

$\sqrt{- 1 (9)}$

Step 3

Rewrite

\sqrt{- 1 (9)}

$\sqrt{- 1 (9)}$ as

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

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

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

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

Step 4

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

i \cdot \sqrt{9}

$i \cdot \sqrt{9}$

Step 5

Rewrite

9

$9$ as

3^{2}

$3^{2}$ .

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

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

Step 6

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

i \cdot 3

$i \cdot 3$

Step 7

Move

3

$3$ to the left of

i

$i$ .

3 i

$3 i$

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

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

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$