Linear Algebra Examples

\sqrt{3^{2} - 2^{2} - 6^{2}}

$\sqrt{3^{2} - 2^{2} - 6^{2}}$

Step 1

Simplify the expression.

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Step 1.1

Raise

3

$3$ to the power of

2

$2$ .

\sqrt{9 - 2^{2} - 6^{2}}

$\sqrt{9 - 2^{2} - 6^{2}}$

Step 1.2

Raise

2

$2$ to the power of

2

$2$ .

\sqrt{9 - 1 \cdot 4 - 6^{2}}

$\sqrt{9 - 1 \cdot 4 - 6^{2}}$

Step 1.3

Multiply

- 1

$- 1$ by

4

$4$ .

\sqrt{9 - 4 - 6^{2}}

$\sqrt{9 - 4 - 6^{2}}$

Step 1.4

Raise

6

$6$ to the power of

2

$2$ .

\sqrt{9 - 4 - 1 \cdot 36}

$\sqrt{9 - 4 - 1 \cdot 36}$

Step 1.5

Multiply

- 1

$- 1$ by

36

$36$ .

\sqrt{9 - 4 - 36}

$\sqrt{9 - 4 - 36}$

Step 1.6

Subtract

4

$4$ from

9

$9$ .

\sqrt{5 - 36}

$\sqrt{5 - 36}$

Step 1.7

Subtract

36

$36$ from

5

$5$ .

\sqrt{- 31}

$\sqrt{- 31}$

\sqrt{- 31}

$\sqrt{- 31}$

Step 2

Rewrite

- 31

$- 31$ as

- 1 (31)

$- 1 (31)$ .

\sqrt{- 1 (31)}

$\sqrt{- 1 (31)}$

Step 3

Rewrite

\sqrt{- 1 (31)}

$\sqrt{- 1 (31)}$ as

\sqrt{- 1} \cdot \sqrt{31}

$\sqrt{- 1} \cdot \sqrt{31}$ .

\sqrt{- 1} \cdot \sqrt{31}

$\sqrt{- 1} \cdot \sqrt{31}$

Step 4

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

i \sqrt{31}

$i \sqrt{31}$

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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