Solve 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 radical in an equation?

Back

To isolate a radical, you can move all other terms to the opposite side of the equation.

Front

What is the first step in solving a radical equation?

Back

Square both sides of the equation to eliminate the radical.

Front

What should you do after squaring both sides of a radical equation?

Back

Simplify the equation and solve for the variable.

Front

Why is it important to check your solutions in radical equations?

Back

Because squaring both sides can introduce extraneous solutions that do not satisfy the original equation.

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

Solve the radical equation: √(x + 9) = 6.

Back

x = 27.

Front

Solve the radical equation: √(2x - 5) = 3.

Back

x = 9.

Front

Solve the radical equation: √(x + 4) = -2.

Back

No solution (the square root cannot be negative).

Front

What is the domain of a radical function?

Back

The set of all possible input values (x) for which the function is defined, typically requiring the expression under the radical to be non-negative.