Solving Radical Equations and Simplifying Expressions

The video tutorial explains how to solve radical equations containing more than one radical. It outlines the steps to isolate radicals on each side of the equation and raise both sides to the power of the index. Two examples are provided, demonstrating the process of solving and verifying solutions. The first example involves solving an equation with two square roots, while the second example further illustrates the method with a different equation. The tutorial emphasizes the importance of checking solutions to ensure accuracy.

What is the first step in solving radical equations with more than one radical?

• Eliminate all radicals immediately

• Put one radical on each side of the equation

• Add a constant to both sides

• Combine all radicals on one side

When solving an equation with two square roots, what operation is performed after isolating the radicals?

• Add the radicals together

• Multiply both sides by the index

• Divide both sides by the index

• Square both sides of the equation

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

• x = 5

• x = 4.5

• x = 3

• x = 9

How can you verify the solution of a radical equation using a calculator?

• By solving for another variable

• By checking if both sides of the equation are equal

• By finding the derivative of the equation

• By graphing the equation

What is the simplified form of the square root of 18?

• 6 square root 3

• 3 square root 2

• 2 square root 3

• 9 square root 2

In the second example, what is the equation after squaring both sides?

• 4x + 9 = 2x + 24

• 2x + 9 = 4x + 24

• 4x + 9 = -2x + 24

• 2x + 9 = -2x + 24

What is the value of x in the second example after solving the equation?

• x = 9/2

• x = 7/2

• x = 3/2

• x = 5/2

How do you verify the solution of the second example?

• By solving a different equation

• By checking the graph of the equation

• By substituting the value back into the original equation

• By using a different variable

What is the result of simplifying the expression 6 over the square root of 2?

• 6 square root 2

• 3 square root 3

• 2 square root 3

• 3 square root 2

What is the common factor used to simplify the fraction 15/6?

• 3

• 5

• 2

• 6