Understanding Radical Equations

In this video, Teacher Smith explains how to solve radical equations through four examples. The video begins with an introduction to the topic and then demonstrates solving equations involving square roots. Each example is explained step-by-step, including checking the solutions. The video covers solving simple square root equations, using transposition, handling complex radicals, and dealing with equations with radicals on both sides. The tutorial concludes with a summary and encourages viewers to subscribe for more content.

What is the first step in solving a radical equation?

• Add a constant to both sides

• Square both sides of the equation

• Multiply both sides by the radical

• Divide both sides by the radical

In the equation √x = 7, what is the value of x?

• 49

• 7

• 14

• 21

How do you verify the solution of √x = 7?

• Substitute x with 14 and check if the equation holds

• Substitute x with 21 and check if the equation holds

• Substitute x with 49 and check if the equation holds

• Substitute x with 7 and check if the equation holds

In the equation √(x + 5) = 11, what is the value of x?

• 36

• 6

• 25

• 16

What is the purpose of transposing terms in an equation?

• To isolate the variable

• To eliminate the radical

• To simplify the equation

• To add complexity to the equation

In the equation √(5x + 1) = 6, what is the value of x?

• 5

• 7

• 6

• 8

How do you verify the solution of √(5x + 1) = 6?

• Substitute x with 8 and check if the equation holds

• Substitute x with 6 and check if the equation holds

• Substitute x with 5 and check if the equation holds

• Substitute x with 7 and check if the equation holds

In the equation √x = √(6x - 5), what is the value of x?

• 4

• 5

• 3

• 2

What is the result of squaring both sides of the equation √x = √(6x - 5)?

• x = 6x + 5

• x = 36x + 25

• x = 6x - 5

• x = 36x - 25

How do you verify the solution of √x = √(6x - 5)?

• Substitute x with 5 and check if the equation holds

• Substitute x with 4 and check if the equation holds

• Substitute x with 2 and check if the equation holds

• Substitute x with 3 and check if the equation holds