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.

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

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

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.

  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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