 ## Related Topics

• Only numbers and expressions that have the same radical part can be added or subtracted.
• Remember, combining “unlike” radical terms is not possible.

## Examples

Simplify: $$6\sqrt{2}+5\sqrt{2}$$

Solution:

Since we have the same radical parts, then we can add these two radicals: Add like terms: $$6\sqrt{2}+5\sqrt{2}=11\sqrt{2}$$

Simplify: $$2\sqrt{8}-2\sqrt{2}$$

Solution:

The two radical parts are not the same. First, we need to simplify the $$2\sqrt{8}$$. Then: $$2\sqrt{8}=2\sqrt{(4×2)}=2(\sqrt{4})(\sqrt{2})=4\sqrt{2}$$. Now, combine like terms: $$2\sqrt{8}-2\sqrt{2}=4\sqrt{2}-2\sqrt{2}=2\sqrt{2}$$

Simplify: $$6\sqrt{5}+3\sqrt{5}$$

Solution:

Add like terms: $$6\sqrt{5}+3\sqrt{5}=9\sqrt{5}$$

Simplify: $$5\sqrt{7}-3\sqrt{7}$$

Solution:

Combine like terms: $$5\sqrt{7}-3\sqrt{7}=2\sqrt{7}$$

1. $$\color{blue}{2\sqrt{6}+\sqrt{6}=}$$
2. $$\color{blue}{3\sqrt{3}+6\sqrt{3}=}$$
3. $$\color{blue}{\sqrt{45}+2\sqrt{5}=}$$
4. $$\color{blue}{6\sqrt{2}-5\sqrt{2}=}$$
5. $$\color{blue}{-2\sqrt{6}-\sqrt{6}=}$$
6. $$\color{blue}{3\sqrt{7}-\sqrt{28}=}$$
1. $$\color{blue}{3\sqrt{6}}$$
2. $$\color{blue}{9\sqrt{3}}$$
3. $$\color{blue}{5\sqrt{5}}$$
4. $$\color{blue}{\sqrt{2}}$$
5. $$\color{blue}{-3\sqrt{6}}$$
6. $$\color{blue}{\sqrt{7}}$$

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