Cube Root

Definition

The cube root is a mathematical operation that finds the value that, when multiplied by itself three times, results in a given number. It is the inverse operation of cubing a number, and is denoted by the symbol $\sqrt[3]{}$.

5 Must Know Facts For Your Next Test

1. The cube root of a number is the value that, when multiplied by itself three times, equals the original number.
2. Cube roots are used to find the side length of a cube given its volume, or to find the volume of a cube given its side length.
3. Cube roots can be positive or negative, as both positive and negative numbers cubed will result in the same positive value.
4. The cube root of 1 is 1, the cube root of -1 is -1, and the cube root of 0 is 0.
5. Cube roots are often used in physics and engineering applications, such as calculating the volume of a cube or the side length of a cube.

Review Questions

• Explain how the cube root operation is the inverse of cubing a number.
  • The cube root operation is the inverse of cubing a number because it finds the value that, when multiplied by itself three times, results in the original number. For example, the cube root of 8 is 2, because 2 multiplied by itself three times equals 8. This inverse relationship means that if you cube a number and then take the cube root of the result, you will end up back at the original number.
• Describe the relationship between the cube root and the volume of a cube.
  • The cube root is closely related to the volume of a cube because the volume of a cube is calculated by multiplying the length of one side by itself three times. Therefore, if you know the volume of a cube, you can find the length of one side by taking the cube root of the volume. Conversely, if you know the length of one side of a cube, you can calculate the volume by cubing that length. This connection between the cube root and the volume of a cube is important in many engineering and physics applications.
• Analyze the significance of the fact that cube roots can be positive or negative, even though the result is always positive.
  • The fact that cube roots can be positive or negative, even though the result is always positive, is significant because it reflects the inverse relationship between cubing a number and taking the cube root. When a number is cubed, both the positive and negative versions of that number will result in the same positive value. For example, both 2 and -2 cubed result in 8. Therefore, the cube root of 8 can be either 2 or -2, since both of those values, when cubed, will equal 8. This property of cube roots is important to understand when working with equations or applications involving cubes and cube roots.

Related terms

Exponent: A mathematical notation that indicates the number of times a value is multiplied by itself. For example, $x^3$ means $x$ multiplied by itself three times.

Radical: A mathematical symbol, $\sqrt{}$, that represents the operation of finding the root of a number. The cube root is a specific type of radical.

Power: The result of raising a number to an exponent. For example, $2^3$ is the power of 2 raised to the 3rd power, which equals 8.