Combining Operations
Now we will simplify some radical expressions that involve more than one
operation.
Example 1
Simplify:
![](./articles_imgs/295/combin47.gif)
Solution |
![](./articles_imgs/295/combin48.gif) |
Factor each radicand.
|
![](./articles_imgs/295/combin49.gif) |
Write each radical as
the product of radicals.
|
![](./articles_imgs/295/combin50.gif) |
Simplify square roots
of perfect squares.
|
![](./articles_imgs/295/combin51.gif) |
For each term, multiply
the radicals. |
![](./articles_imgs/295/combin52.gif) |
Combine like radical
terms.
|
![](./articles_imgs/295/combin53.gif) |
Therefore, |
![](./articles_imgs/295/combin54.gif) |
Example 2
Simplify:
![](./articles_imgs/295/combin55.gif)
Solution |
![](./articles_imgs/295/combin56.gif) |
To remove the parentheses,
distribute
|
![](./articles_imgs/295/combin58.gif) |
Multiply
by
Then
factor the radicand.
|
![](./articles_imgs/295/combin61.gif) |
Simplify the second term:
|
![](./articles_imgs/295/combin63.gif) |
Combine like radical terms.
|
![](./articles_imgs/295/combin64.gif) |
Thus, |
![](./articles_imgs/295/combin65.gif) |
|