How do you simplify (sqrt12 - 4 ) - ( 8 + sqrt27 )?

Mar 4, 2018

See a solution process below:

Explanation:

First, remove all of the terms from parenthesis. Be careful to handle the signs of each individual term correctly:

$\sqrt{12} - 4 - 8 - \sqrt{27}$

Next, group like terms:

$\sqrt{12} - \sqrt{27} - 4 - 8$

Then, combine like terms:

$\sqrt{12} - \sqrt{27} - 12$

Now, use this rule of radicals to simplify and combine the radicals:

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

$\sqrt{\textcolor{red}{4} \cdot \textcolor{b l u e}{3}} - \sqrt{\textcolor{red}{9} \cdot \textcolor{b l u e}{3}} - 12$

$\sqrt{\textcolor{red}{4}} \sqrt{\textcolor{b l u e}{3}} - \sqrt{\textcolor{red}{9}} \sqrt{\textcolor{b l u e}{3}} - 12$

$2 \sqrt{\textcolor{b l u e}{3}} - 3 \sqrt{\textcolor{b l u e}{3}} - 12$

$\left(2 - 3\right) \sqrt{\textcolor{b l u e}{3}} - 12$

$- 1 \sqrt{\textcolor{b l u e}{3}} - 12$

$- \sqrt{\textcolor{b l u e}{3}} - 12$

Or

$- 12 - \sqrt{\textcolor{b l u e}{3}}$