# How do you simplify 5sqrt17+17sqrt5?

Sep 4, 2016

$5 \sqrt{17} + 17 \sqrt{5}$ is already in simplest form.

#### Explanation:

The numbers $5$ and $17$ are unrelated primes, so it is not possible to combine their square roots to simplify this expression.

If you wished, you could express it differently as:

$5 \sqrt{17} + 17 \sqrt{5} = {\sqrt{5}}^{2} \sqrt{17} + {\sqrt{17}}^{2} \sqrt{5}$

$\textcolor{w h i t e}{5 \sqrt{17} + 17 \sqrt{5}} = \sqrt{5} \sqrt{17} \left(\sqrt{5} + \sqrt{17}\right)$

$\textcolor{w h i t e}{5 \sqrt{17} + 17 \sqrt{5}} = \sqrt{85} \left(\sqrt{5} + \sqrt{17}\right)$

but I would not call that simpler.