Addition and Subtraction Using Radical Notation

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  • 0:02 One of These Things Is…
  • 0:25 Like Terms with Radicals
  • 0:49 Add and Subtract Radicals
  • 2:45 Lesson Summary
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Lesson Transcript
Instructor: Jennifer Beddoe

Jennifer has an MS in Chemistry and a BS in Biological Sciences.

There are specific rules governing adding and subtracting radical expressions. This lesson will describe these rules and give examples of how they are used.

One of These Things Is Not Like the Other

Remember that song from the kids show, it went something like, 'One of these things is not like the other. One of these things just doesn't belong?' Then, the point was to look at four items and determine which one of them was different, either because of color, shape or some other characteristic. There are times in your study of algebra when you will have to look at different terms and determine which of them are alike and which are different.

Like Terms with Radicals

Terms containing radicals, or square roots, are considered like terms if the portion of the terms under the radical symbols is the same. These are like terms:




These are not like terms:




Add and Subtract Radicals

In order to add and subtract expressions with radicals, they must be like terms. If the portions under each radical are different, they cannot be combined using addition or subtraction. If the portions under the radicals are the same, then to add or subtract simply add or subtract the number in front of the radical symbol leaving what is under the radical the same.

Here's an example. Simplify:


Because both of these terms have a square root of 2, they can be added together to get 6√2. How about this one?


Again, since both terms have a 7 under the square root symbol, they can be combined to get 4√7. Let's try one more example.


In this example, because one of the terms under the radical is a 5 and the other is a 2, they cannot be combined and the expression is as simplified as it can be.

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