Simplify the Radical Expression 5/(10- square root of 5)

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

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

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

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

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

Expand the denominator using the FOIL method.

$\frac{5 (10 + \sqrt{5})}{100 + 10 \sqrt{5} - 10 \sqrt{5} - {\sqrt{5}}^{2}}$

Simplify.

$\frac{5 (10 + \sqrt{5})}{95}$

Cancel the common factors.

Factor $5$ out of $95$ .

$\frac{5 (10 + \sqrt{5})}{5 \cdot 19}$

Cancel the common factor.

$\frac{5 (10 + \sqrt{5})}{5 \cdot 19}$

Rewrite the expression.

$\frac{10 + \sqrt{5}}{19}$

The result can be shown in multiple forms.

Exact Form:

$\frac{10 + \sqrt{5}}{19}$

Decimal Form:

$0.64400357 \dots$