Trigonometry Examples

$5 \sqrt{12} - 9 \sqrt{48}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $12$ as $2^{2} \cdot 3$ .

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Step 1.1.1

Factor $4$ out of $12$ .

$5 \sqrt{4 (3)} - 9 \sqrt{48}$

Step 1.1.2

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

$5 \sqrt{2^{2} \cdot 3} - 9 \sqrt{48}$

$5 \sqrt{2^{2} \cdot 3} - 9 \sqrt{48}$

Step 1.2

Pull terms out from under the radical.

$5 (2 \sqrt{3}) - 9 \sqrt{48}$

Step 1.3

Multiply $2$ by $5$ .

$10 \sqrt{3} - 9 \sqrt{48}$

Step 1.4

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 1.4.1

Factor $16$ out of $48$ .

$10 \sqrt{3} - 9 \sqrt{16 (3)}$

Step 1.4.2

Rewrite $16$ as $4^{2}$ .

$10 \sqrt{3} - 9 \sqrt{4^{2} \cdot 3}$

$10 \sqrt{3} - 9 \sqrt{4^{2} \cdot 3}$

Step 1.5

Pull terms out from under the radical.

$10 \sqrt{3} - 9 (4 \sqrt{3})$

Step 1.6

Multiply $4$ by $- 9$ .

$10 \sqrt{3} - 36 \sqrt{3}$

$10 \sqrt{3} - 36 \sqrt{3}$

Step 2

Subtract $36 \sqrt{3}$ from $10 \sqrt{3}$ .

$- 26 \sqrt{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$- 26 \sqrt{3}$

Decimal Form:

$- 45.03332099 \dots$

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