Radical and Quadratic Equations

The video tutorial explains how to solve a radical equation by first isolating the radical and then cubing both sides to eliminate it. This transforms the equation into a quadratic form, which is then solved by factoring. The solutions are found using the zero property, and verification is suggested by substituting the solutions back into the original equation.

What is the first step in solving a radical equation where the radical is already isolated?

• Multiply both sides by the radical

• Raise both sides to the power of the radical

• Add a constant to both sides

• Subtract a constant from both sides

When you raise a cubed root to the third power, what do you obtain?

• The square of the argument

• The argument itself

• The reciprocal of the argument

• The cube of the argument

What method is used to factor the quadratic equation x^2 - 16 = 0?

• Synthetic division

• Quadratic formula

• Difference of squares

• Completing the square

What are the solutions to the equation x^2 - 16 = 0?

• x = 0 and x = 16

• x = 4 and x = -4

• x = 8 and x = -8

• x = 2 and x = -2

Why is it unnecessary to check the solutions obtained after cubing both sides of the equation?

• Because the solutions are verified by graphing

• Because the solutions are verified by the quadratic formula

• Because cubing both sides does not introduce extraneous solutions

• Because the solutions are always correct