# How do you simplify 2sqrt24 - sqrt50 + 5sqrt54 - sqrt18?

Apr 19, 2018

$19 \sqrt{6} - 8 \sqrt{2}$

#### Explanation:

$2 \sqrt{24} - \sqrt{50} + 5 \sqrt{54} - \sqrt{18}$
$= \left(2 \cdot \sqrt{4} \cdot \sqrt{6}\right) - \left(\sqrt{25} \cdot \sqrt{2}\right) + \left(5 \cdot \sqrt{9} \cdot \sqrt{6}\right) - \left(\sqrt{9} \cdot \sqrt{2}\right)$
$= \left(2 \cdot 2 \cdot \sqrt{6}\right) - \left(5 \cdot \sqrt{2}\right) + \left(5 \cdot 3 \cdot \sqrt{6}\right) - \left(3 \cdot \sqrt{2}\right)$
$= \left(4 \sqrt{6}\right) - \left(5 \sqrt{2}\right) + \left(15 \sqrt{6}\right) - \left(3 \sqrt{2}\right)$
$= \left(4 \sqrt{6}\right) + \left(15 \sqrt{6}\right) - \left(5 \sqrt{2}\right) - \left(3 \sqrt{2}\right)$
$= 19 \sqrt{6} - 8 \sqrt{2}$

First, we want to break up the radicand by into its factors. You want to be able to write it in terms of the radicand of a number that can be rationally squared (step 1). For example $\sqrt{9} = 3$. After this, you can simplify by squaring these types of numbers (step 2) and by multiplying the whole numbers (step 3). Then rearrange the equation to add like terms together. Remember you can only add them together if they share the same radicand (step 4). This would simplify it further down to the final answer.