Trigonometry Examples

$\frac{\sqrt{2}}{4} \cdot \frac{\sqrt{6}}{4}$

Step 1

Multiply $\frac{\sqrt{2}}{4} \cdot \frac{\sqrt{6}}{4}$ .

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Step 1.1

Multiply $\frac{\sqrt{2}}{4}$ by $\frac{\sqrt{6}}{4}$ .

$\frac{\sqrt{2} \sqrt{6}}{4 \cdot 4}$

Step 1.2

Combine using the product rule for radicals.

$\frac{\sqrt{2 \cdot 6}}{4 \cdot 4}$

Step 1.3

Multiply $2$ by $6$ .

$\frac{\sqrt{12}}{4 \cdot 4}$

Step 1.4

Multiply $4$ by $4$ .

$\frac{\sqrt{12}}{16}$

Step 2

Simplify the numerator.

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Step 2.1

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

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Step 2.1.1

Factor $4$ out of $12$ .

$\frac{\sqrt{4 (3)}}{16}$

Step 2.1.2

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

$\frac{\sqrt{2^{2} \cdot 3}}{16}$

Step 2.2

Pull terms out from under the radical.

$\frac{2 \sqrt{3}}{16}$

Step 3

Cancel the common factor of $2$ and $16$ .

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Step 3.1

Factor $2$ out of $2 \sqrt{3}$ .

$\frac{2 (\sqrt{3})}{16}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Factor $2$ out of $16$ .

$\frac{2 \sqrt{3}}{2 \cdot 8}$

Step 3.2.2

Cancel the common factor.

$\frac{2 \sqrt{3}}{2 \cdot 8}$

Step 3.2.3

Rewrite the expression.

$\frac{\sqrt{3}}{8}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$\frac{\sqrt{3}}{8}$

Decimal Form:

$0.21650635 \dots$