Section 5.4: Solving Radical Equations

Front

What is a radical equation?

Back

An equation that contains a variable within a radical (square root, cube root, etc.).

Front

How do you solve a radical equation?

Back

Isolate the radical on one side, then square both sides to eliminate the radical, and solve for the variable.

Front

Why is it important to check your answers when solving radical equations?

Back

To ensure that the solutions are valid and do not produce extraneous solutions.

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving the equation but does not satisfy the original equation.

Front

What is the first step in solving the equation √(x + 4) = 3?

Back

Square both sides to eliminate the radical: x + 4 = 9.

Front

Solve the radical equation: √(x - 1) = 5.

Back

x - 1 = 25, so x = 26.

Front

What happens if you square both sides of an equation incorrectly?

Back

You may introduce extraneous solutions that do not satisfy the original equation.

Front

Solve the radical equation: √(2x + 3) = 7.

Back

2x + 3 = 49, so 2x = 46, and x = 23.

Front

What is the solution to the equation √(x) = -3?

Back

No solution, because the square root of a number cannot be negative.

Front

How do you handle radical equations with multiple radicals?

Back

Isolate one radical, square both sides, and repeat as necessary until all radicals are eliminated.