# How do you simplify 4sqrt 27-11sqrt 20-sqrt48+7sqrt45?

Jul 15, 2017

See a solution process below:

#### Explanation:

First, rewrite the terms within the radicals as:

$4 \sqrt{9 \cdot 3} - 11 \sqrt{4 \cdot 5} - \sqrt{16 \cdot 3} + 7 \sqrt{9 \cdot 5}$

We can now use this rule of radicals to simplify the radicals:

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

$4 \sqrt{9} \sqrt{3} - 11 \sqrt{4} \sqrt{5} - \sqrt{16} \sqrt{3} + 7 \sqrt{9} \sqrt{5} \implies$

$\left(4 \cdot 3 \sqrt{3}\right) - \left(11 \cdot 2 \sqrt{5}\right) - 4 \sqrt{3} + \left(7 \cdot 3 \sqrt{5}\right) \implies$

$12 \sqrt{3} - 22 \sqrt{5} - 4 \sqrt{3} + 21 \sqrt{5}$

We can now group and combine like terms:

$12 \sqrt{3} - 4 \sqrt{3} - 22 \sqrt{5} + 21 \sqrt{5} \implies$

$\left(12 - 4\right) \sqrt{3} + \left(- 22 + 21\right) \sqrt{5} \implies$

$8 \sqrt{3} + \left(- 1\right) \sqrt{5} \implies$

$8 \sqrt{3} - \sqrt{5}$