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Fourth Root

LAST UPDATE: April 8th, 2018

4th Root Calculator

What is a fourth root?

The fourth root of a number is the number that would have to be multiplied by itself 4 times to get the original number.
For example, the fourth root of 81 is 3 as 3 x 3 x 3 x 3 is 81.
The fourth root of 104,976 is 18, as 18 x 18 x 18 x 18 is 104,976.

How to calculate the fourth root

Even for perfect fourth root numbers, the fourth root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the fourth root of 4,096
1) Try a number – 5 : 5 x 5 x 5 x 5 = 625 (too low)
2) Try another number that is more than 5 – 6 : 6 x 6 x 6 x 6 = 1,296 (too low)
3) Try a number that is more than 6 – 10 – 10 x 10 x 10 x 10 = 10,000 (too high)
4) Try a number in between 6 and 10 – 8 – 8 x 8 x 8 x 8 = 4,096 (answer)
A fourth root can also be calculated as the same number to the exponent 1/4.
4√number = number1/4

Table – Fourth Root (4√) of 1 – 100

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