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

What is the first step to solve the radical equation √(x + 5) = 7?

Back

Square both sides to eliminate the square root.

Front

What does it mean to 'undo' a square root in an equation?

Back

To 'undo' a square root means to square both sides of the equation.

Front

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

Back

To ensure that the solutions are valid and not extraneous.

Front

What is an extraneous solution?

Back

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

Front

How do you isolate a radical in an equation?

Back

By performing inverse operations to move other terms to the opposite side.

Front

What is the process to solve the equation 2√(x) = 16?

Back

Divide both sides by 2, then square both sides to solve for x.

Front

What is the solution to the equation √(x - 3) = 5?

Back

x = 28.

Front

What is the general form of a radical equation?

Back

An equation of the form √(f(x)) = g(x), where f(x) and g(x) are expressions involving x.

Front

What should you do if you encounter a radical equation with multiple radicals?

Back

Isolate one radical at a time and square both sides to eliminate it.