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Ch 10.3Solving Radical Equations
Objective:
To solve equations involving square roots (and equations involving perfect
squares).
Definitions
Radical Equation:
An equation involving the radical/square root symbol √
Extraneous Solution:
A solution that is NOT valid
Steps for Solvingradical (√) equations
1. Isolate the radical using the reverse order of operations.
2. Square both sides (the radical & the squared symbol cancel each other out)
3. Isolate the variable on one side & solve
4. Check your answers for extraneous solutions.
Equations with Extraneous SolutionsNote: The solution obtained by squaring both sides of the equation is not valid in the original equation.
Check:
No solution
Problem!
An isolated radical cannot equal a negative!
Examples of Radical Equations
1) 2)
3) 4)
5) 6)
More examples of Radical Equations
Solve. Check for extraneous solutions.
7)
Solve. Check for extraneous solutions.
8)
Steps for SolvingSquared ( )² equations
1. Isolate the variable on one side.
2. If it is squared, take the square root (√) of both sides.
3. Add the +/- sign in front of one of the square root symbols (±√)
For example: 2 + x² = 6Step 1 -2 -2
x² = 4Step 2 √x² = ±√4 x =
±2
Solve the Rational Equations. Check for extraneous solutions.
Solve.
One Solution
Two Solutions