Trigonometry Examples

$2 \sqrt{3} (\sqrt{8} - 5 \sqrt{6})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1.1

Factor $4$ out of $8$ .

$2 \sqrt{3} (\sqrt{4 (2)} - 5 \sqrt{6})$

Step 1.1.2

Rewrite $4$ as $2^{2}$ .

$2 \sqrt{3} (\sqrt{2^{2} \cdot 2} - 5 \sqrt{6})$

$2 \sqrt{3} (\sqrt{2^{2} \cdot 2} - 5 \sqrt{6})$

Step 1.2

Pull terms out from under the radical.

$2 \sqrt{3} (2 \sqrt{2} - 5 \sqrt{6})$

$2 \sqrt{3} (2 \sqrt{2} - 5 \sqrt{6})$

Step 2

Apply the distributive property.

$2 \sqrt{3} (2 \sqrt{2}) + 2 \sqrt{3} (- 5 \sqrt{6})$

Step 3

Multiply $2 \sqrt{3} (2 \sqrt{2})$ .

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Step 3.1

Multiply $2$ by $2$ .

$4 \sqrt{3} \sqrt{2} + 2 \sqrt{3} (- 5 \sqrt{6})$

Step 3.2

Combine using the product rule for radicals.

$4 \sqrt{2 \cdot 3} + 2 \sqrt{3} (- 5 \sqrt{6})$

Step 3.3

Multiply $2$ by $3$ .

$4 \sqrt{6} + 2 \sqrt{3} (- 5 \sqrt{6})$

$4 \sqrt{6} + 2 \sqrt{3} (- 5 \sqrt{6})$

Step 4

Multiply $2 \sqrt{3} (- 5 \sqrt{6})$ .

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Step 4.1

Multiply $- 5$ by $2$ .

$4 \sqrt{6} - 10 \sqrt{3} \sqrt{6}$

Step 4.2

Combine using the product rule for radicals.

$4 \sqrt{6} - 10 \sqrt{6 \cdot 3}$

Step 4.3

Multiply $6$ by $3$ .

$4 \sqrt{6} - 10 \sqrt{18}$

$4 \sqrt{6} - 10 \sqrt{18}$

Step 5

Simplify each term.

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Step 5.1

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 5.1.1

Factor $9$ out of $18$ .

$4 \sqrt{6} - 10 \sqrt{9 (2)}$

Step 5.1.2

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

$4 \sqrt{6} - 10 \sqrt{3^{2} \cdot 2}$

$4 \sqrt{6} - 10 \sqrt{3^{2} \cdot 2}$

Step 5.2

Pull terms out from under the radical.

$4 \sqrt{6} - 10 (3 \sqrt{2})$

Step 5.3

Multiply $3$ by $- 10$ .

$4 \sqrt{6} - 30 \sqrt{2}$

$4 \sqrt{6} - 30 \sqrt{2}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$4 \sqrt{6} - 30 \sqrt{2}$

Decimal Form:

$- 32.62844790 \dots$

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