7.5 Solving Radical Equations Notes
When solving radical equations, the main goal is to isolate and get rid of the radical. Once you do that, you
will be left with a basic equation to solve. We can get rid of a square root by squaring or get rid of cube
roots by cubing.
Warning: Squaring both sides of your equation can sometimes create extraneous solutions.
Extraneous solutions may only appear if the radical’s index is _______________.
Check for extraneous solutions by substituting your solution(s):
1) Into the “non-radical” side.
2) Inside the radical.
Problem
Check
Example #1:
√3𝑥 − 5 = −2
Example #2:
√5𝑥 + 2
3= 3
Example #3:
√𝑥 + 2 = 𝑥
If negative, then it is extraneous! (Throw it out!)
Positive is okay. (Keep it!)
