Trigonometry Examples

$\sqrt{18^{2} + {(\sqrt{3})}^{2}}$

Step 1

Raise $18$ to the power of $2$ .

$\sqrt{324 + {(\sqrt{3})}^{2}}$

Step 2

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

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Step 2.1

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

$\sqrt{324 + {(3^{\frac{1}{2}})}^{2}}$

Step 2.2

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

$\sqrt{324 + 3^{\frac{1}{2} \cdot 2}}$

Step 2.3

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

$\sqrt{324 + 3^{\frac{2}{2}}}$

Step 2.4

Cancel the common factor of $2$ .

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Step 2.4.1

Cancel the common factor.

$\sqrt{324 + 3^{\frac{2}{2}}}$

Step 2.4.2

Rewrite the expression.

$\sqrt{324 + 3^{1}}$

Step 2.5

Evaluate the exponent.

$\sqrt{324 + 3}$

Step 3

Add $324$ and $3$ .

$\sqrt{327}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\sqrt{327}$

Decimal Form:

$18.08314132 \dots$