Radical Equations and Extraneous Solutions

The video tutorial explains how to solve a radical equation with one square root. It outlines the steps to isolate the radical, square both sides, and solve the resulting quadratic equation by factoring. The tutorial emphasizes the importance of checking solutions to ensure they satisfy the original equation, highlighting the concept of extraneous solutions. The final solution is verified, and any extraneous solutions are identified and discarded.

What is the first step in solving a radical equation with one square root?

• Isolate the radical

• Combine like terms

• Check for extraneous solutions

• Factor the equation

When squaring both sides of the equation, what should you be careful not to do?

• Add new terms

• Square each term individually

• Subtract from both sides

• Multiply by zero

After simplifying the squared equation, what type of equation do you typically get?

• Exponential equation

• Linear equation

• Quadratic equation

• Cubic equation

What is the purpose of setting the quadratic equation to zero?

• To isolate the variable

• To solve by factoring

• To simplify the equation

• To check for extraneous solutions

Which of the following is a potential factor of the quadratic equation in this problem?

• 5x + 2

• 3x + 5

• 4x + 9

• 2x + 7

Why is it important to check the solutions in the original equation?

• To find the exact value

• To ensure they are not extraneous

• To simplify the equation further

• To verify the quadratic formula

What is an extraneous solution?

• A solution that satisfies the original equation

• A solution that does not satisfy the original equation

• A solution that is a decimal

• A solution that is negative

What was the result of checking the solution x = 9/4 in the original equation?

• It satisfied the original equation

• It was a decimal solution

• It was a negative solution

• It was an extraneous solution

What was the result of checking the solution x = 9/2 in the original equation?

• It was an extraneous solution

• It was a decimal solution

• It satisfied the original equation

• It was a negative solution

What is the final solution to the radical equation?

• x = 0

• x = 9/4

• x = 9/2

• x = 1