Solve Radical Equations

Front

What is a radical equation?

Back

A radical equation is an equation in which a variable is contained within a radical (square root, cube root, etc.).

Front

How do you isolate a variable in a radical equation?

Back

To isolate a variable in a radical equation, you typically 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 = 9?

Back

The first step is to square both sides of the equation to eliminate the square root, resulting in x = 81.

Front

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

Back

To solve, square both sides to get x - 3 = 25, then add 3 to both sides to find x = 28.

Front

What should you check after solving a radical equation?

Back

You should check your solutions by substituting them back into the original equation to ensure they do not create extraneous solutions.

Front

What is an extraneous solution?

Back

An extraneous solution is a solution that emerges from the process of solving the equation but does not satisfy the original equation.

Front

How do you solve the equation x = √(x + 7)?

Back

Square both sides to get x^2 = x + 7, rearrange to form a quadratic equation x^2 - x - 7 = 0, and then use the quadratic formula to find x.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a), used to find the solutions of a quadratic equation ax² + bx + c = 0.

Front

What is the importance of the domain in radical equations?

Back

The domain is important because it defines the set of possible values for the variable that make the equation valid, especially since square roots cannot be negative.

Front

How do you solve the equation √(2x + 3) = 7?

Back

Square both sides to get 2x + 3 = 49, then solve for x by subtracting 3 and dividing by 2, resulting in x = 23.