# How do you evaluate (4+√50) - (3-√8)?

Mar 10, 2018

See a solution process below:

#### Explanation:

First, we can rewrite the expression as:

$4 + \sqrt{50} - 3 + \sqrt{8} \implies$

$4 - 3 + \sqrt{50} + \sqrt{8} \implies$

$1 + \sqrt{50} + \sqrt{8}$

Next, we can rewrite the radicals as:

$1 + \sqrt{25 \cdot 2} + \sqrt{4 \cdot 2}$

Then, we can use this rule for radicals to simplify the radicals:

$\sqrt{\textcolor{red}{a} \cdot \textcolor{b l u e}{b}} = \sqrt{\textcolor{red}{a}} \cdot \sqrt{\textcolor{b l u e}{b}}$

$1 + \sqrt{\textcolor{red}{25} \cdot \textcolor{b l u e}{2}} + \sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{2}} \implies$

$1 + \sqrt{\textcolor{red}{25}} \sqrt{\textcolor{b l u e}{2}} + \sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{2}} \implies$

$1 + 5 \sqrt{\textcolor{b l u e}{2}} + 2 \sqrt{\textcolor{b l u e}{2}}$

Now, we can factor out the common term to complete the evaluation:

$1 + \left(5 + 2\right) \sqrt{\textcolor{b l u e}{2}}$

$1 + 7 \sqrt{\textcolor{b l u e}{2}}$