Adding and Subtracting Square Roots
The procedure for adding and subtracting square roots which
may contain algebraic expressions is very similar to the one we
usewhen adding and subtracting numerical square roots:
- simplify the square root in each term of the expression
- combine terms whose square roots are identical
Read the following examples:
Example 1:
Simplify 
solution:
We have
Thus
as the final answer.
The method should be fairly obvious by now. Use the remaining
three examples as practice problems. Try to do them yourself
before looking at our solutions.
Example 2:
Simplify 
solution:
First, we check to simplify each of the two square roots
individually:
Thus
as the final answer.
Example 3:
Simplify 
solution:
So
as the final answer.
Example 4:
Simplify 
solution:
Each square root must first be simplified:
and
Therefore
This is as simple as we can get the expression.
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