Combining Like Radical Terms
Adding and subtracting radical expressions is like adding and subtracting
polynomials.
• With polynomials, to add like
terms, we add their coefficients. |
2x + 3x = (2 + 3)x = 5x |
• With radical expressions, to add
like radical terms, we add the
numbers in front of the radicals. |
![](./articles_imgs/294/combin17.gif) |
Before we can combine radical terms, we sometimes need to simplify the
individual radicals to obtain like terms.
Consider this example: |
![](./articles_imgs/294/combin18.gif) |
At first glance, we may think we cannot add the radical terms because the
radicands are different. |
However, if we simplify
, we can
combine like radical terms: |
![](./articles_imgs/294/combin20.gif) |
Example 2
Simplify:
![](./articles_imgs/294/combin21.gif)
Solution
First simplify
![](./articles_imgs/294/combin22.gif)
The radicand, 75y, has a perfect
square factor, 25. |
![](./articles_imgs/294/combin23.gif) |
Replace
with
|
![](./articles_imgs/294/combin26.gif) |
Combine the like radical terms,
|
![](./articles_imgs/294/combin28.gif) |
Simplify. |
![](./articles_imgs/294/combin29.gif) |
So, |
![](./articles_imgs/294/combin30.gif) |
Example 3
Simplify:
![](./articles_imgs/294/combin31.gif)
Solution
First simplify
![](./articles_imgs/294/combin32.gif)
The radicand, 54x, has a perfect
cube factor, 27. |
![](./articles_imgs/294/combin33.gif) |
Replace
![](./articles_imgs/294/combin34.gif) |
![](./articles_imgs/294/combin35.gif) |
Multiply
![](./articles_imgs/294/combin36.gif) |
![](./articles_imgs/294/combin37.gif) |
Combine the like radical terms
|
![](./articles_imgs/294/combin39.gif) |
Simplify. |
![](./articles_imgs/294/combin40.gif) |
So, |
![](./articles_imgs/294/combin41.gif) |
|