# How to Add and Subtract Radical Expressions? (+FREE Worksheet!)

To add and subtract radical Expressions, you need to follow a few simple tips, which in this article will be taught to you along with examples.

## Related Topics

- How to Multiply Radical Expressions
- How to Rationalize Radical Expressions
- How to Solve Radical Equations
- How to Simplify Radical Expressions
- How to Find Domain and Range of Radical Functions

## Adding and Subtracting Radical Expressions

- Only numbers and expressions that have the same radical part can be added or subtracted.
- Remember, combining “unlike” radical terms is not possible.
- For numbers with the same radical part, just add or subtract factors outside the radicals

## Examples

### Adding and Subtracting Radical Expressions – Example 1:

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: \(6\sqrt{2}+5\sqrt{2}=11\sqrt{2}\)

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### Adding and Subtracting Radical Expressions – Example 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: \(2\sqrt{8}-2\sqrt{2}=4\sqrt{2}-2\sqrt{2}=2\sqrt{2}\)

### Adding and Subtracting Radical Expressions – Example 3:

Simplify: \(6\sqrt{5}+3\sqrt{5}\)

**Solution:**

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

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### Adding and Subtracting Radical Expressions – Example 4:

Simplify: \(5\sqrt{7}-3\sqrt{7}\)

**Solution:**

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

## Exercises for Adding and Subtracting Radical Expressions

### Add and Subtract Radical Expressions.

- \(\color{blue}{2\sqrt{6}+\sqrt{6}=}\)
- \(\color{blue}{3\sqrt{3}+6\sqrt{3}=}\)
- \(\color{blue}{\sqrt{45}+2\sqrt{5}=}\)
- \(\color{blue}{6\sqrt{2}-5\sqrt{2}=}\)
- \(\color{blue}{-2\sqrt{6}-\sqrt{6}=}\)
- \(\color{blue}{3\sqrt{7}-\sqrt{28}=}\)

- \(\color{blue}{3\sqrt{6}}\)
- \(\color{blue}{9\sqrt{3}}\)
- \(\color{blue}{5\sqrt{5}}\)
- \(\color{blue}{\sqrt{2}}\)
- \(\color{blue}{-3\sqrt{6}}\)
- \(\color{blue}{\sqrt{7}}\)

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