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. |
 |
Before we can combine radical terms, we sometimes need to simplify the
individual radicals to obtain like terms.
| Consider this example: |
 |
| 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: |
 |
Example 2
Simplify:
Solution
First simplify
| The radicand, 75y, has a perfect
square factor, 25. |
 |
Replace
 with
 |
 |
Combine the like radical terms,
 |
 |
| Simplify. |
 |
| So, |
 |
Example 3
Simplify:
Solution
First simplify
| The radicand, 54x, has a perfect
cube factor, 27. |
 |
Replace
 |
 |
Multiply
 |
 |
Combine the like radical terms
 |
 |
| Simplify. |
 |
| So, |
 |
|
