Trigonometry Examples

$2 (\frac{\sqrt{13}}{4}) (- \frac{\sqrt{5}}{4})$

Step 1

Cancel the common factor of $2$ .

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Step 1.1

Move the leading negative in $- \frac{\sqrt{5}}{4}$ into the numerator.

$2 (\frac{\sqrt{13}}{4}) \cdot \frac{- \sqrt{5}}{4}$

Step 1.2

Factor $2$ out of $4$ .

$2 (\frac{\sqrt{13}}{4}) \cdot \frac{- \sqrt{5}}{2 (2)}$

Step 1.3

Cancel the common factor.

$2 \frac{\sqrt{13}}{4} \cdot \frac{- \sqrt{5}}{2 \cdot 2}$

Step 1.4

Rewrite the expression.

$\frac{\sqrt{13}}{4} \cdot \frac{- \sqrt{5}}{2}$

Step 2

Multiply $\frac{\sqrt{13}}{4}$ by $\frac{- \sqrt{5}}{2}$ .

$\frac{\sqrt{13} (- \sqrt{5})}{4 \cdot 2}$

Step 3

Combine using the product rule for radicals.

$\frac{- \sqrt{13 \cdot 5}}{4 \cdot 2}$

Step 4

Simplify the expression.

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Step 4.1

Multiply $13$ by $5$ .

$\frac{- \sqrt{65}}{4 \cdot 2}$

Step 4.2

Multiply $4$ by $2$ .

$\frac{- \sqrt{65}}{8}$

Step 4.3

Move the negative in front of the fraction.

$- \frac{\sqrt{65}}{8}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$- \frac{\sqrt{65}}{8}$

Decimal Form:

$- 1.00778221 \dots$