Radical and Quadratic Equations

This video tutorial focuses on solving radical equations with one radical. It outlines the steps to isolate the radical, raise both sides to the power of the index, solve, and check for extraneous solutions. The video explains why raising to the power of the index simplifies the equation and provides several examples, including solving equations with square and cube roots. The importance of checking solutions to identify extraneous ones is emphasized. The tutorial concludes with a preview of the next video, which will cover equations with two radicals.

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

• Add a constant to both sides

• Isolate the radical on one side

• Subtract a constant from both sides

• Multiply both sides by the index

Why is it important to check solutions in radical equations?

• To simplify the equation further

• To verify the index of the radical

• To ensure no extraneous solutions are included

• To find the exact value of the radical

What operation is performed to eliminate a square root in an equation?

• Adding the index

• Subtracting the index

• Squaring both sides

• Taking the cube root

What is the result of squaring the square root of x?

• x

• 2x

• x squared

• Square root of x

In the first example, what is the value of x after solving the equation?

• 11

• 128

• 121

• 7

In the second example, what is the value of x when the equation is solved?

• 47

• 7

• 49

• 47/3

What is the cube root of 64?

• 8

• 4

• 16

• 2

In the quadratic equation example, what are the potential solutions for x?

• x = 4 and x = 9

• x = 6 and x = 12

• x = 3 and x = 7

• x = 5 and x = 10

Which solution was found to be extraneous in the quadratic equation example?

• x = 12

• x = 9

• x = 4

• x = 6

Why is it crucial to check solutions in the quadratic equation example?

• To simplify the equation further

• To verify the index of the radical

• To confirm the equation is quadratic

• To ensure the solutions satisfy the original equation