Solving Radical Equations and Extraneous Solutions

The video tutorial explains how to solve equations containing radicals by isolating the radical, raising both sides to the power of the index, and solving the resulting equation. It includes two examples, demonstrating the process of checking solutions to identify extraneous solutions. The importance of verifying solutions is emphasized to ensure accuracy.

What is the first step in solving an equation with one radical?

• Multiply both sides by the index

• Isolate the radical on one side

• Subtract a constant from both sides

• Add a constant to both sides

In the first example, what operation is performed after isolating the square root?

• Adding a constant to both sides

• Dividing both sides by the index

• Subtracting a constant from both sides

• Squaring both sides of the equation

What is the result of squaring the square root of (X + 6)?

• X + 12

• X + 6

• 2X + 6

• X^2 + 6

What type of equation is formed after squaring both sides in the first example?

• Linear equation

• Exponential equation

• Quadratic equation

• Cubic equation

Which of the following is an extraneous solution in the first example?

• X = -5

• X = -2

• X = 4

• X = 0

Why is it important to check solutions in radical equations?

• To find the derivative

• To ensure no extraneous solutions

• To simplify the equation

• To factor the equation

What is the first step in solving the second example equation?

• Multiply both sides by 2

• Divide both sides by 2

• Add 1 to both sides

• Subtract 1 from both sides

In the second example, what is the result of squaring the square root of (4X + 9)?

• 8X + 18

• 4X + 9

• 16X + 81

• 2X + 9

What is the correct solution for the second example equation?

• X = 2

• X = 0

• X = 4

• X = -2

Which solution is extraneous in the second example?

• X = 1

• X = -2

• X = 4

• X = 3