Fourth Root

Definition

The fourth root of a number is the value that, when raised to the power of four, results in the original number. It is a mathematical operation that is used to find the value that, when multiplied by itself four times, equals the given number.

5 Must Know Facts For Your Next Test

1. The fourth root of a number is denoted by the symbol $\sqrt[4]{}$, where the number inside the radical is the value for which the fourth root is being calculated.
2. To find the fourth root of a number, you can use the inverse operation of raising a number to the power of four, which is taking the fourth root.
3. The fourth root of a number is the same as raising that number to the power of $\frac{1}{4}$.
4. The fourth root of a number is often used in various mathematical and scientific applications, such as in the calculation of volume, surface area, and other geometric properties.
5. The fourth root can be used to find the value of a number that, when raised to the power of four, equals a given value, similar to how the square root is used to find the value that, when squared, equals a given value.

Review Questions

• Explain the relationship between the fourth root and raising a number to the power of one-fourth.
  • The fourth root of a number is the same as raising that number to the power of one-fourth. This is because the fourth root is the value that, when multiplied by itself four times, equals the original number. Raising a number to the power of one-fourth is the inverse operation, where the original number is raised to a fractional power to find the value that, when multiplied by itself four times, results in the original number.
• Describe how the fourth root can be used to calculate geometric properties, such as volume and surface area.
  • The fourth root can be used to calculate various geometric properties, such as volume and surface area, because these properties often involve raising a number to the power of four. For example, the volume of a cube is calculated by raising the length of one side to the power of three, and the surface area of a cube is calculated by raising the length of one side to the power of two. By taking the fourth root of the volume or surface area, you can find the length of one side of the cube, which is a crucial piece of information for many geometric calculations and applications.
• Analyze the significance of the fourth root in the context of higher roots and their applications in mathematics and science.
  • The fourth root is an important concept within the broader context of higher roots, which are mathematical operations that find the value that, when raised to a power greater than two, equals the original number. The fourth root, in particular, is significant because it is often used in various mathematical and scientific applications, such as in the calculation of volume, surface area, and other geometric properties. Additionally, the fourth root can be used to find the value of a number that, when raised to the power of four, equals a given value, similar to how the square root is used to find the value that, when squared, equals a given value. The ability to work with higher roots, including the fourth root, is an essential skill in many fields of mathematics and science, as it allows for the analysis and manipulation of complex numerical relationships.

Related terms

Square Root: The square root of a number is the value that, when multiplied by itself, equals the original number.

Cube Root: The cube root of a number is the value that, when multiplied by itself three times, equals the original number.

Higher Roots: Higher roots, such as the fourth root, are mathematical operations that find the value that, when raised to a power greater than two, equals the original number.