Trigonometry Examples

v ({(- 3 \sqrt{3})}^{2} + 9)

$v ({(- 3 \sqrt{3})}^{2} + 9)$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to

- 3 \sqrt{3}

$- 3 \sqrt{3}$ .

v ({(- 3)}^{2} {\sqrt{3}}^{2} + 9)

$v ({(- 3)}^{2} {\sqrt{3}}^{2} + 9)$

Step 1.2

Raise

- 3

$- 3$ to the power of

2

$2$ .

v (9 {\sqrt{3}}^{2} + 9)

$v (9 {\sqrt{3}}^{2} + 9)$

Step 1.3

Rewrite

{\sqrt{3}}^{2}

${\sqrt{3}}^{2}$ as

3

$3$ .

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Step 1.3.1

Use

\sqrt[n]{a^{x}} = a^{\frac{x}{n}}

$\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite

\sqrt{3}

$\sqrt{3}$ as

3^{\frac{1}{2}}

$3^{\frac{1}{2}}$ .

v (9 {(3^{\frac{1}{2}})}^{2} + 9)

$v (9 {(3^{\frac{1}{2}})}^{2} + 9)$

Step 1.3.2

Apply the power rule and multiply exponents,

{(a^{m})}^{n} = a^{m n}

${(a^{m})}^{n} = a^{m n}$ .

v (9 \cdot 3^{\frac{1}{2} \cdot 2} + 9)

$v (9 \cdot 3^{\frac{1}{2} \cdot 2} + 9)$

Step 1.3.3

Combine

\frac{1}{2}

$\frac{1}{2}$ and

2

$2$ .

v (9 \cdot 3^{\frac{2}{2}} + 9)

$v (9 \cdot 3^{\frac{2}{2}} + 9)$

Step 1.3.4

Cancel the common factor of

2

$2$ .

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Step 1.3.4.1

Cancel the common factor.

v (9 \cdot 3^{\frac{2}{2}} + 9)

$v (9 \cdot 3^{\frac{2}{2}} + 9)$

Step 1.3.4.2

Rewrite the expression.

v (9 \cdot 3^{1} + 9)

$v (9 \cdot 3^{1} + 9)$

v (9 \cdot 3^{1} + 9)

$v (9 \cdot 3^{1} + 9)$

Step 1.3.5

Evaluate the exponent.

v (9 \cdot 3 + 9)

$v (9 \cdot 3 + 9)$

v (9 \cdot 3 + 9)

$v (9 \cdot 3 + 9)$

Step 1.4

Multiply

9

$9$ by

3

$3$ .

v (27 + 9)

$v (27 + 9)$

v (27 + 9)

$v (27 + 9)$

Step 2

Simplify the expression.

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Step 2.1

Add

27

$27$ and

9

$9$ .

v \cdot 36

$v \cdot 36$

Step 2.2

Move

36

$36$ to the left of

v

$v$ .

36 v

$36 v$

36 v

$36 v$

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

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