Trigonometry Examples

$3 (2 + \sqrt{27})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $27$ as $3^{2} \cdot 3$ .

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Step 1.1.1

Factor $9$ out of $27$ .

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

Step 1.1.2

Rewrite $9$ as $3^{2}$ .

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

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

Step 1.2

Pull terms out from under the radical.

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

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

Step 2

Simplify by multiplying through.

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Step 2.1

Apply the distributive property.

$3 \cdot 2 + 3 (3 \sqrt{3})$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $3$ by $2$ .

$6 + 3 (3 \sqrt{3})$

Step 2.2.2

Multiply $3$ by $3$ .

$6 + 9 \sqrt{3}$

$6 + 9 \sqrt{3}$

$6 + 9 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$6 + 9 \sqrt{3}$

Decimal Form:

$21.58845726 \dots$

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