Solving Equations Using Cube Roots

This lesson teaches how to solve equations of the form x cubed equals p, where p is a positive rational number. Using a practical example of determining the dimensions of a chocolate cube with a volume of 64 cubic centimeters, the lesson demonstrates the process of isolating the variable by taking the cube root of both sides of the equation. The solution is verified by substituting back into the original equation, confirming that each side length of the chocolate cube should be 4 centimeters. The lesson concludes with a recap of solving cubic equations.

What is the volume of each chocolate cube that the candy company wants to create?

• 16 cubic centimeters

• 128 cubic centimeters

• 64 cubic centimeters

• 32 cubic centimeters

Which mathematical operation is used to isolate the variable in the equation x cubed equals 64?

• Square root

• Subtraction

• Cube root

• Addition

What is the side length of the chocolate cube when the volume is 64 cubic centimeters?

• 5 centimeters

• 2 centimeters

• 3 centimeters

• 4 centimeters

How do we verify that the side length of the chocolate cube is correct?

• By checking if 4 times 4 equals 64

• By checking if 4 squared equals 64

• By checking if 4 cubed equals 64

• By checking if 4 plus 4 equals 64

What is the final step to ensure the solution to the equation is correct?

• Multiply both sides by 4

• Subtract 4 from both sides

• Divide both sides by 4

• Substitute the solution back into the original equation