Basic Math Examples

$\frac{6}{\sqrt{2} + 5}$

Step 1

Multiply $\frac{6}{\sqrt{2} + 5}$ by $\frac{\sqrt{2} - 5}{\sqrt{2} - 5}$ .

$\frac{6}{\sqrt{2} + 5} \cdot \frac{\sqrt{2} - 5}{\sqrt{2} - 5}$

Step 2

Multiply $\frac{6}{\sqrt{2} + 5}$ by $\frac{\sqrt{2} - 5}{\sqrt{2} - 5}$ .

$\frac{6 (\sqrt{2} - 5)}{(\sqrt{2} + 5) (\sqrt{2} - 5)}$

Step 3

Expand the denominator using the FOIL method.

$\frac{6 (\sqrt{2} - 5)}{{\sqrt{2}}^{2} + \sqrt{2} \cdot - 5 + 5 \sqrt{2} - 25}$

Step 4

Simplify.

$\frac{6 (\sqrt{2} - 5)}{- 23}$

Step 5

Move the negative in front of the fraction.

$- \frac{6 (\sqrt{2} - 5)}{23}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{6 (\sqrt{2} - 5)}{23}$

Decimal Form:

$0.93542254 \dots$