Trigonometry Examples

$\frac{5}{\sqrt{10} + \sqrt{5}}$

Step 1

Multiply $\frac{5}{\sqrt{10} + \sqrt{5}}$ by $\frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} - \sqrt{5}}$ .

$\frac{5}{\sqrt{10} + \sqrt{5}} \cdot \frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} - \sqrt{5}}$

Step 2

Multiply $\frac{5}{\sqrt{10} + \sqrt{5}}$ by $\frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} - \sqrt{5}}$ .

$\frac{5 (\sqrt{10} - \sqrt{5})}{(\sqrt{10} + \sqrt{5}) (\sqrt{10} - \sqrt{5})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (\sqrt{10} - \sqrt{5})}{{\sqrt{10}}^{2} - \sqrt{50} + \sqrt{50} - {\sqrt{5}}^{2}}$

Step 4

Simplify.

$\frac{5 (\sqrt{10} - \sqrt{5})}{5}$

Step 5

Cancel the common factor of $5$ .

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Step 5.1

Cancel the common factor.

$\frac{5 (\sqrt{10} - \sqrt{5})}{5}$

Step 5.2

Divide $\sqrt{10} - \sqrt{5}$ by $1$ .

$\sqrt{10} - \sqrt{5}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$\sqrt{10} - \sqrt{5}$

Decimal Form:

$0.92620968 \dots$