Enter any number or integer into the calculator to determine the 5th root.

Fifth Root Formula

The following formula is used to calculate a fifth root:

5√ X = X ^ 1/5 = Y

  • Where Y is the fifth root
  • X is the integer that the fifth root was taken of

To calculate the fifth root, raise the number to the power of 1 over 5.

What is a fifth root?

A fifth root is defined as a number multiplied by itself five times, yielding the original number that the fifth root was taken of.

How to calculate fifth root?

Example Problem:

The following example outlines how to calculate the fifth root.

First, determine the number or integer to take the fifth root of. In this example, the number is 125.

Next, raise that number to (1/5).

125 ^ 1/5 = 2.6265

Check that when multiplied by itself 5 times, this equals the original number of 125:

2.6265*2.6265* 2.6265 * 2.6265 * 2.6265 = 125.

FAQ

What is the difference between a fifth root and a square root?

A fifth root is a number that, when multiplied by itself four more times (for a total of five multiplications), gives the original number. In contrast, a square root is a number that, when multiplied by itself once (for a total of two multiplications), gives the original number. Essentially, a fifth root is a more specific and less commonly used calculation compared to the more familiar square root.

Can negative numbers have a fifth root?

Yes, negative numbers can have a fifth root. Unlike even roots, such as square roots, which cannot be applied to negative numbers (in the realm of real numbers), odd roots, including the fifth root, can be applied to negative numbers. For example, the fifth root of -32 is -2, because when -2 is multiplied by itself four more times, the result is -32.

How do calculators compute the fifth root of a number?

Calculators typically use iterative approximation algorithms to compute the fifth root of a number. These algorithms start with an initial guess and then refine that guess through a series of iterations until they arrive at a value that, when raised to the fifth power, closely matches the original number. This process is very fast and can produce highly accurate results.