Evaluate 5/(1+ square root of 10)

$\frac{5}{1 + \sqrt{10}}$

Step 1

Multiply $\frac{5}{1 + \sqrt{10}}$ by $\frac{1 - \sqrt{10}}{1 - \sqrt{10}}$ .

$\frac{5}{1 + \sqrt{10}} \cdot \frac{1 - \sqrt{10}}{1 - \sqrt{10}}$

Step 2

Multiply $\frac{5}{1 + \sqrt{10}}$ by $\frac{1 - \sqrt{10}}{1 - \sqrt{10}}$ .

$\frac{5 (1 - \sqrt{10})}{(1 + \sqrt{10}) (1 - \sqrt{10})}$

Step 3

Expand the denominator using the FOIL method.

$\frac{5 (1 - \sqrt{10})}{1 - \sqrt{10} + \sqrt{10} - {\sqrt{10}}^{2}}$

Step 4

Simplify.

$\frac{5 (1 - \sqrt{10})}{- 9}$

Step 5

Move the negative in front of the fraction.

$- \frac{5 (1 - \sqrt{10})}{9}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{5 (1 - \sqrt{10})}{9}$

Decimal Form:

$1.20126536 \dots$