Chapter 7 – Powers, Roots, and Radicals7.3 – Solving Radical Equations

7.3 – Solving Radical EquationsToday we will be:

Solving equations that contain radicals or rational exponents

7.3 – Solving Radical EquationsRadical equation – an equation that contains

radicals with the variable in the radicand.

√(x + 6) = 5

7.3 – Solving Radical EquationsSolving Radical Equations

Isolate the radical on one side of the equation, if needed.

Raise each side of the equation to the same power to eliminate the radical.

Solve the resulting equation using techniques that you learned in previous chapters.

Check your solution.

7.3 – Solving Radical EquationsExample 1

Solve 3√y – 4 = 0

7.3 – Solving Radical EquationsExample 2

2√(x + 12) – 3 = 5.

7.3 – Solving Radical EquationsTo solve an equation with two radicals, first

rewrite the equation so that each side has only one radical. Then raise each side of the equation to the same power.

7.3 – Solving Radical EquationsExample 3

Solve √3x - √(x + 6) = 0.

7.3 – Solving Radical EquationsExtraneous solution – an apparent solution

that does not make the original equation true.

Raising each side of an equation to the same power can lead to solutions that do not make the original equation true.

You must check each apparent solution in the original equation

Any solution that does not satisfy the original equation is extraneous

7.3 – Solving Radical EquationsExample 4

Solve x = √(x + 12). Check for extraneous solutions.

7.3 – Solving Radical EquationsWhen an equation contains a power with a

rational exponent, you solve the equation the same way you would solve a radical equation. Isolate the power on one side of the equation

Raise each side of the equation to the reciprocal of the rational exponent

Solve for the variable

7.3 – Solving Radical EquationsExample 5

Solve x2/3 – 9 = 16. Check for extraneous solutions.

7.3 – Solving Radical Equations

HOMEWORK

7.3 Worksheet