# What is (5 -(sqrt)2) (3 + sqrt 2)?

Sep 18, 2015

$13 + 2 \sqrt{2}$

#### Explanation:

First we must expand the equation of $\left(5 - \sqrt{2}\right) \left(3 + \sqrt{2}\right)$. And we will get the equation be like;

$\left(5 - \sqrt{2}\right) \left(3 + \sqrt{2}\right)$

$= 5 \left(3\right) + 5 \left(\sqrt{2}\right) - 3 \left(\sqrt{2}\right) - \sqrt{2} \left(\sqrt{2}\right)$

Note that for $\sqrt{2} \left(\sqrt{2}\right)$, we can calculate it by;

$= \sqrt{2} \times \sqrt{2} = {\left(2\right)}^{\frac{1}{2}} \times {\left(2\right)}^{\frac{1}{2}} = {2}^{\frac{1}{2} + \frac{1}{2}} = {2}^{1} = 2$

And we will get;

$= 15 + 5 \sqrt{2} - 3 \sqrt{2} - 2$

$5 \sqrt{2}$ can subtract $3 \sqrt{2}$ since it has the same base, which is $\sqrt{2}$. Calculate all of it and we will get;

$= 13 + 2 \sqrt{2}$