# How do you simplify sqrt5/(7-sqrt5)?

May 16, 2018

$\frac{1}{44} \left(5 + 7 \sqrt{5}\right)$

#### Explanation:

$\frac{\sqrt{5}}{7 - \sqrt{5}}$

$= \frac{\sqrt{5}}{7 - \sqrt{5}} \times \frac{7 + \sqrt{5}}{7 + \sqrt{5}}$

$= \frac{7 \sqrt{5} + 5}{49 - 5}$

$\frac{1}{44} \left(5 + 7 \sqrt{5}\right)$

May 16, 2018

$\frac{7 \setminus \sqrt{5} + 5}{54}$

#### Explanation:

$\setminus \frac{\sqrt{5}}{7 - \setminus \sqrt{5}}$
To remove the square root in the denominator, multiply by its conjugate:
\sqrt(5)/(7-\sqrt(5))*(7+\sqrt(5))/(7+\sqrt(5))=(\sqrt(5)(7+\sqrt(5)))/((7-\sqrt(5))(7+\sqrt(5))

Now simplify that.
$\frac{7 \setminus \sqrt{5} + 5}{49 + \setminus \cancel{7 \setminus \sqrt{5} - 7 \setminus \sqrt{5}} + 5}$
$\frac{7 \setminus \sqrt{5} + 5}{49 + 5} = \setminus \textcolor{\to m a \to}{\frac{7 \setminus \sqrt{5} + 5}{54}}$