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 isolate a variable in a radical equation?

Back

Square both sides of the equation to eliminate the radical, then solve for the variable.

Front

What is the first step in solving the equation √(x + 5) = 7?

Back

Square both sides to get x + 5 = 49.

Front

What is the solution to the equation √(x + 5) = 7?

Back

x = 44.

Front

What should you do after solving a radical equation?

Back

Check your solution by substituting it back into the original equation.

Front

What is the extraneous solution in radical equations?

Back

A solution that does not satisfy the original equation after substitution.

Front

Solve the equation √(2x - 3) = 5.

Back

x = 14.

Front

What is the domain of the function f(x) = √(x - 2)?

Back

x must be greater than or equal to 2.

Front

How do you solve the equation √(x + 1) + 3 = 6?

Back

Isolate the radical: √(x + 1) = 3, then square both sides to find x = 8.

Front

What is the principle of squaring both sides of an equation?

Back

It allows you to eliminate the radical, but you must check for extraneous solutions.