# How do you add and subtract radicals?

##### 1 Answer
Apr 6, 2018

To add and subtract radicals, they must be the same radical

#### Explanation:

Given: How do you add and subtract radicals?

To add and subtract radicals, they must be the same radical

Example1: $\sqrt{5} + 2 \sqrt{5} = 3 \sqrt{5}$

Example 2: $6 \sqrt{2} - 2 \sqrt{2} = 4 \sqrt{2}$

If you can simplify the square root by using perfect squares to make them the same radical, do it using $\sqrt{m \cdot n} = \sqrt{m} \cdot \sqrt{n}$

Example 3: $6 \sqrt{8} - 2 \sqrt{2}$

Simplify $\sqrt{8} : \text{ } \sqrt{8} = \sqrt{4} \cdot \sqrt{2} = 2 \sqrt{2}$

$6 \sqrt{8} - 2 \sqrt{2} = 6 \cdot 2 \sqrt{2} - 2 \sqrt{2} = 12 \sqrt{2} - 2 \sqrt{2} = 10 \sqrt{2}$