Trigonometry Examples

$2 \sqrt{6 - 4} \sqrt{16 + 3} \sqrt{54}$

Step 1

Subtract $4$ from $6$ .

$2 \sqrt{2} \sqrt{16 + 3} \sqrt{54}$

Step 2

Add $16$ and $3$ .

$2 \sqrt{2} \sqrt{19} \sqrt{54}$

Step 3

Multiply $2 \sqrt{2} \sqrt{19}$ .

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Step 3.1

Combine using the product rule for radicals.

$2 \sqrt{19 \cdot 2} \sqrt{54}$

Step 3.2

Multiply $19$ by $2$ .

$2 \sqrt{38} \sqrt{54}$

$2 \sqrt{38} \sqrt{54}$

Step 4

Rewrite $54$ as $3^{2} \cdot 6$ .

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Step 4.1

Factor $9$ out of $54$ .

$2 \sqrt{38} \sqrt{9 (6)}$

Step 4.2

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

$2 \sqrt{38} \sqrt{3^{2} \cdot 6}$

$2 \sqrt{38} \sqrt{3^{2} \cdot 6}$

Step 5

Pull terms out from under the radical.

$2 \sqrt{38} (3 \sqrt{6})$

Step 6

Multiply $2 \sqrt{38} (3 \sqrt{6})$ .

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Step 6.1

Multiply $3$ by $2$ .

$6 \sqrt{38} \sqrt{6}$

Step 6.2

Combine using the product rule for radicals.

$6 \sqrt{6 \cdot 38}$

Step 6.3

Multiply $6$ by $38$ .

$6 \sqrt{228}$

$6 \sqrt{228}$

Step 7

Rewrite $228$ as $2^{2} \cdot 57$ .

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Step 7.1

Factor $4$ out of $228$ .

$6 \sqrt{4 (57)}$

Step 7.2

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

$6 \sqrt{2^{2} \cdot 57}$

$6 \sqrt{2^{2} \cdot 57}$

Step 8

Pull terms out from under the radical.

$6 (2 \sqrt{57})$

Step 9

Multiply $2$ by $6$ .

$12 \sqrt{57}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$12 \sqrt{57}$

Decimal Form:

$90.59801322 \dots$

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