Math 11 Pre-Calculus Chapters 5: Radical Expressions and Equations

5.3: Radical Equations (Day 1)

Objectives: Solving equations involving square roots Determining the roots of a radical equation algebraically Identifying restrictions on the values for the variable in a radical equation

Today’s lesson is about solving radical equations. Radical Equations are equations with radical signs in them. Solving a radical equation is similar to solving a linear or quadratic equation, we are trying to isolate the variable and determine possible values for the unknown. Example 1) a) State the restrictions on x in 5+√2 x+1=12 if the radical is a real number.

b) Solve 5+√2 x+1=12

Your Turn

Identify any restrictions on y in −2+√ y−1=3 if the radical is a real number. Then, solve the equation.

Math 11 Pre-Calculus Chapters 5: Radical Expressions and Equations

Example 2) Identify the restrictions on n in n−√5−n=-7 if the radical is a real number. Then, solve the equation.

Your TurnIdentify any restrictions on m in m−√2m+3=6 if the radical is a real number. Then, solve the equation. Check your solution(s).

To solve radical equations:

1. State any restrictions on the variables.

Math 11 Pre-Calculus Chapters 5: Radical Expressions and Equations

2. Isolate the radical. Square both sides.3. Solve the remaining quadratic equation.4. Check your solution(s). Reject any extraneous roots.

Recall that extraneous roots are solutions that do not satisfy any initial conditions.

Example 3) Solve 7+√3 x=√5 x+4+5 , x ≥ 0. Check your solution.