Week 4 – Adding and Subtracting Radicals

To add or subtract radicals, you combine like terms. The radicand and index must be the same. Only the coefficient will change.

Simplify:

$\sqrt{108}+\sqrt{45}+\sqrt{80}-\sqrt{27}$

First, you need to change the entire radicals to mixed radicals.

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

$6\sqrt{3}$ and $-3\sqrt{3}$ are like terms because they have the same radicand and the same index.

$3\sqrt{5}$ and $4\sqrt{5}$ are also like terms and can be combined.

So, $3\sqrt{3}+7\sqrt{5}$