Understanding Radical Equations

The video tutorial explains how to solve radical equations using a four-step process: isolating the radical, raising both sides to the nth power, solving for the variable, and checking for extraneous solutions. It provides three examples, demonstrating the process and addressing potential pitfalls, such as extraneous solutions. The tutorial emphasizes the importance of verifying solutions, especially when dealing with square roots, due to their limited domains.

What is the first step in solving a radical equation?

• Solve for the variable

• Check for extraneous solutions

• Isolate the radical

• Raise both sides to the nth power

When dealing with a square root, to what power should both sides of the equation be raised?

• 1

• 2

• 3

• 4

In the example where the radical is already isolated, what is the value of x when the equation is solved?

• 7

• 2

• 49

• 51

What happens when you square both sides of an equation with a square root?

• The radicals are doubled

• The equation becomes quadratic

• The radicals are eliminated

• The equation becomes linear

What is the result of squaring the square root of 49?

• 7

• 49

• 14

• 0

In the example where x is found to be 4, what was the original equation?

• x minus 2 equals 7

• Square root of x equals 2

• Square root of 2x minus 1 equals negative 3

• 3 times the square root of x equals 6

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

• To ensure the equation is balanced

• To verify the solution is within the domain

• To simplify the equation

• To find the nth power

Which type of radical equation is more likely to have extraneous solutions?

• Fourth root

• Square root

• Fifth root

• Cube root

In the example where the equation has no solution, what was the incorrect assumption made?

• The equation was not squared

• The variable was not solved

• The radical was not isolated

• The square root can be negative

What is the correct solution for the equation: square root of 2x minus 1 equals negative 3?

• No solution

• x = 10

• x = 5

• x = 3