Radical and Exponential Equations

The video tutorial covers solving radical equations, starting with square roots and moving to higher power roots like the fourth root. It explains the process of isolating the radical, squaring both sides, and validating solutions to ensure they are not extraneous. The tutorial also demonstrates solving equations using different methods, such as taking both positive and negative square roots and using the difference of squares.

What is the first step in solving a radical equation?

• Multiply both sides by a constant

• Add a constant to both sides

• Isolate the radical

• Subtract a constant from both sides

After isolating the square root in the equation \( \sqrt{x+2} - 2 = 0 \), what should be done next?

• Take the square root of both sides

• Subtract 2 from both sides

• Add 2 to both sides

• Square both sides

What is the principal root of 4?

• 4

• 3

• 2

• 1

How do you solve an equation involving a fourth root?

• Square both sides

• Cube both sides

• Raise both sides to the fourth power

• Take the fourth root of both sides

What is the equivalent expression for the fourth root of \( x^2 - 9 \)?

• \( (x^2 - 9)^2 \)

• \( (x^2 - 9)^{1/4} \)

• \( (x^2 - 9)^{1/2} \)

• \( (x^2 - 9)^4 \)

What is the result of raising 2 to the fourth power?

• 12

• 8

• 16

• 20

When solving \( x^2 = 25 \), what are the possible values of x?

• 5

• 5 and -5

• 0

• -5

What is the form called when an equation is written as \( x^2 - 25 = 0 \)?

• Sum of squares

• Linear form

• Difference of squares

• Quadratic form

Why is it important to check for extraneous solutions in radical equations?

• To find additional solutions

• To simplify the equation further

• To verify the solutions satisfy the original equation

• To ensure all solutions are positive

What is the fourth root of 16?

• 2

• 4

• 16

• 8