Radical and Quadratic Equations

The video tutorial explains how to solve radical equations by isolating the radical, raising both sides to the power of the index, and solving the resulting equation. It provides two examples: one involving a cube root and another involving a fourth root. The first example demonstrates solving a cube root equation and verifying the solution. The second example involves solving a fourth root equation that results in a quadratic equation, which is solved by factoring. Both solutions are verified by substitution into the original equations.

What is the first step in solving a radical equation?

• Subtract a constant from both sides

• Multiply both sides by the index

• Add a constant to both sides

• Isolate the radical on one side

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

• Squaring both sides

• Cubing both sides

• Taking the square root of both sides

• Dividing both sides by 3

What is the solution for x in the equation with the cube root?

• x = 9

• x = 27

• x = 3

• x = 14

In the second example, what is the index of the radical?

• 2

• 3

• 4

• 5

What is the result of raising 2 to the fourth power in the second example?

• 12

• 8

• 20

• 16

What type of equation is formed after removing the fourth root in the second example?

• Quadratic equation

• Cubic equation

• Exponential equation

• Linear equation

Which of the following is a factor of the quadratic equation in the second example?

• x + 4

• x + 6

• x - 8

• x - 2

What is one of the solutions for x in the second example?

• x = -8

• x = 8

• x = 4

• x = -4

What is the other solution for x in the second example?

• x = -6

• x = 6

• x = -2

• x = 2

Why is it important to verify solutions in radical equations?

• To simplify the equation further

• To ensure the equation is balanced

• To find additional solutions

• To confirm the solutions satisfy the original equation