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 & solve4. 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 = 6

Step 1 -2 -2 x² = 4

Step 2 √x² = ±√4 x = ±2

Solve the Rational Equations. Check for extraneous solutions.

Solve.

One SolutionTwo Solutions