# How do you simplify sqrt48-sqrt45-sqrt75+sqrt150?

Aug 30, 2017

See a solution process below:

#### Explanation:

First, we can rewrite the expression as:

$\sqrt{16 \cdot 3} - \sqrt{9 \cdot 5} - \sqrt{25 \cdot 3} + \sqrt{25 \cdot 6}$

Next, we can use this rule of radicals to simplify each radical term individually:

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

$\sqrt{\textcolor{red}{16} \cdot \textcolor{b l u e}{3}} - \sqrt{\textcolor{red}{9} \cdot \textcolor{b l u e}{5}} - \sqrt{\textcolor{red}{25} \cdot \textcolor{b l u e}{3}} + \sqrt{\textcolor{red}{25} \cdot \textcolor{b l u e}{6}} =$

$\sqrt{\textcolor{red}{16}} \cdot \sqrt{\textcolor{b l u e}{3}} - \sqrt{\textcolor{red}{9}} \cdot \sqrt{\textcolor{b l u e}{5}} - \sqrt{\textcolor{red}{25}} \cdot \sqrt{\textcolor{b l u e}{3}} + \sqrt{\textcolor{red}{25}} \cdot \sqrt{\textcolor{b l u e}{6}} =$

$4 \sqrt{3} - 3 \sqrt{5} - 5 \sqrt{3} + 5 \sqrt{6}$

Now, we can group and combine like terms this way:

$4 \sqrt{3} - 5 \sqrt{3} - 3 \sqrt{5} + 5 \sqrt{6} =$

$\left(4 - 5\right) \sqrt{3} - 3 \sqrt{5} + 5 \sqrt{6} =$

$- 1 \sqrt{3} - 3 \sqrt{5} + 5 \sqrt{6} =$

$- \sqrt{3} - 3 \sqrt{5} + 5 \sqrt{6}$

Or, we can group and combine like terms this way:

$4 \sqrt{3} - 3 \sqrt{5} + 5 \left(- \sqrt{3} + \sqrt{6}\right) =$

$- 3 \sqrt{5} + 4 \sqrt{3} + 5 \left(\sqrt{6} - \sqrt{3}\right) =$