Solving Radical Equations and Fractions

The video tutorial explains how to solve a radical equation involving a cube root. It begins by isolating the radical term, then proceeds to solve the equation by cubing both sides. The exact solution is found and expressed as both an improper fraction and a decimal. The tutorial emphasizes the importance of verifying the solution by substituting it back into the original equation to ensure correctness.

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

• Multiply both sides by a constant

• Isolate the radical on one side

• Add a constant to both sides

• Divide both sides by a constant

After isolating the radical, what operation is performed next?

• Multiply both sides by the radical

• Add a constant to both sides

• Divide both sides by the coefficient of the radical

• Subtract a constant from both sides

What is the result of simplifying 10 divided by 10 in the context of the equation?

• 0

• 1

• 10

• 100

What is the purpose of cubing both sides of the equation?

• To balance the equation

• To isolate the variable

• To eliminate the radical

• To simplify the equation

How is the exact solution expressed after solving for x?

• As a whole number

• As an improper fraction

• As a mixed number

• As a decimal

What is the rounded decimal form of the solution?

• 5.027

• 5.03

• 5.02700

• 5.0270

What is the common denominator used to add fractions in this problem?

• 100

• 10

• 1000

• 10000

Why is it important to verify the solution of a radical equation?

• To determine if the solution is positive

• To check if the solution is a fraction

• To confirm the solution satisfies the original equation

• To ensure the solution is a whole number

What is the cube root of 27 thousandths?

• Two-tenths

• One-tenth

• Nine-tenths

• Three-tenths

What is the final step in verifying the solution?

• Substituting the solution back into the original equation

• Dividing the solution by the original equation

• Multiplying the solution by the original equation

• Subtracting the solution from the original equation