# How do you divide sqrt7/(sqrt34+5)?

Mar 24, 2015

This can be simplified a bit by removing the radical from the denominator.
To do this recall that
$\left(a + b\right) \cdot \left(a - b\right) = \left({a}^{2} - {b}^{2}\right)$
or, for our particular case
$\left(\sqrt{34} + 5\right) \cdot \left(\sqrt{34} - 5\right) = 34 - 25 = 9$

Applying this to the original problem:
$\frac{\sqrt{7}}{\sqrt{34} + 5}$

$= \frac{\sqrt{7}}{\sqrt{34} + 5} \cdot \frac{\sqrt{34} - 5}{\sqrt{34} - 5}$

$= \frac{\left(\sqrt{7}\right) \left(\sqrt{34} - 5\right)}{9}$

(The numerator could be multiplied but doing so provides not obvious simplification.)