ch 10.3 solving radical equations objective: to solve equations involving square roots (and...

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