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Solving Radical Equations, Schemes and Mind Maps of Consumer Law

Detailed notes on solving radical equations, which is a crucial topic in mathematics. The main goal is to isolate and eliminate the radical term, leaving a basic equation to solve. Important concepts such as squaring both sides to get rid of square roots, cubing to eliminate cube roots, and checking for extraneous solutions. It includes several examples that illustrate the step-by-step process of solving different types of radical equations. This resource would be highly valuable for students studying algebra, pre-calculus, or any mathematics course that involves working with radical expressions and equations.

Typology: Schemes and Mind Maps

2019/2020

Uploaded on 09/13/2023

khaliddodo05
khaliddodo05 🇺🇸

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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!)
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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: (^) √ 3 𝑥 − 5 = − 2 Example #2: (^) √^3 5 𝑥 + 2 = 3 Example #3: (^) √𝑥 + 2 = 𝑥 If negative, then it is extraneous! (Throw it out!) Positive is okay. (Keep it!)

Example #4: (^) 𝑟 − 6 = √ 21 − 4 𝑟 Example #5: (^) √^3 𝑥 + 1 = √^33 𝑥 − 5 Example #6: (^) √^5 5 𝑥 − 2 = 25 √𝑥 − 1