Solving Radical Equations and Verification

The video tutorial covers solving radical equations, starting with simple examples and progressing to more complex ones. It explains the process of removing radicals by squaring both sides of the equation, checking for extraneous solutions, and verifying the validity of solutions. The tutorial also includes solving a quadratic equation derived from a radical equation and emphasizes the importance of verifying solutions against the original equation.

What is the first step in solving a radical equation?

• Divide both sides by a variable

• Remove the radical by squaring both sides

• Multiply both sides by a constant

• Add a constant to both sides

In the equation √(x² + 7) = 4, what is the result after squaring both sides?

• x² + 7 = 8

• x² + 7 = 4

• x² + 7 = 16

• x² + 7 = 0

What are extraneous solutions?

• Solutions that are always positive

• Solutions that satisfy the original equation

• Solutions that are always negative

• Solutions that do not satisfy the original equation

How do you verify if a solution is valid for a radical equation?

• By checking if it is an integer

• By checking if it is a negative number

• By checking if it is a positive number

• By checking if it satisfies the original equation

What is the equation for the second example?

• √(x + 7) - √(3x - 2) = 1

• √(x + 7) = √(3x - 2)

• √(x + 7) + √(3x - 2) = 1

• √(x + 7) = 1

Why do we transpose terms in the second example?

• To divide the equation

• To simplify the equation

• To eliminate negative terms

• To add more terms

What happens when you square both sides of the equation √(x + 7) = 1 + √(3x - 2)?

• The radicals are eliminated

• The equation becomes more complex

• The equation remains the same

• The equation becomes a linear equation

What type of equation do we solve after simplifying the expression in the second example?

• Linear equation

• Quadratic equation

• Cubic equation

• Exponential equation

What is the correct solution for the second example after verification?

• x = 9

• x = 2

• x = 5

• x = 7