Trigonometry Examples

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

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

Step 1

Simplify each term.

Tap for more steps...

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

$3$ .

Tap for more steps...

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

$2$ .

Tap for more steps...

Step 1.3.4.1

Cancel the common factor.

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

Step 1.3.4.2

Rewrite the expression.

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

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

Step 1.3.5

Evaluate the exponent.

$v (9 \cdot 3 - 9)$

$v (9 \cdot 3 - 9)$

Step 1.4

Multiply

$9$ by

$3$ .

$v (27 - 9)$

$v (27 - 9)$

Step 2

Simplify the expression.

Tap for more steps...

Step 2.1

Subtract

$9$ from

$27$ .

$v \cdot 18$

Step 2.2

Move

$18$ to the left of

$v$ .

$18 v$

$18 v$

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