Understanding Perfect Cubes and Cube Roots

The video tutorial explains how to determine if a number is a perfect cube and how to find its cube root. It compares perfect squares and perfect cubes, highlighting their similarities and differences. The tutorial also discusses the relationship between volume and perfect cubes, providing examples and calculations. Finally, it includes practice problems to reinforce the concepts learned.

What is a perfect cube?

• A number that can be expressed as the cube of an integer.

• A number that can be expressed as the square of an integer.

• A number that can be expressed as the fourth power of an integer.

• A number that can be expressed as the fifth power of an integer.

Which of the following numbers is a perfect cube?

• 12

• 10

• 8

• 5

How is the volume of a cube related to its side length?

• Volume is twice the side length.

• Volume is the square of the side length.

• Volume is the cube of the side length.

• Volume is half the side length.

What is the cube root symbol?

• A square root symbol with a 2 above it.

• A square root symbol with a 5 above it.

• A square root symbol with a 3 above it.

• A square root symbol with a 4 above it.

If a cube has a side length of 3, what is its volume?

• 18

• 36

• 9

• 27

What is the cube root of 64?

• 5

• 2

• 3

• 4

Is 827 a perfect cube?

• Yes, because its cube root is an integer.

• No, because it is a multiple of 10.

• No, because its cube root is not an integer.

• Yes, because it is a multiple of 9.