Trigonometry Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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Step 1.2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3}$ as $3^{\frac{1}{2}}$ .

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

Step 1.2.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 1.2.3

Combine $\frac{1}{2}$ and $2$ .

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

Step 1.2.4

Cancel the common factor of $2$ .

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Step 1.2.4.1

Cancel the common factor.

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

Step 1.2.4.2

Rewrite the expression.

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

Step 1.2.5

Evaluate the exponent.

$v (9 + 3)$

Step 2

Simplify the expression.

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Step 2.1

Add $9$ and $3$ .

$v \cdot 12$

Step 2.2

Move $12$ to the left of $v$ .

$12 v$