5th Root Calculator
Definition – What is a fifth root?
The fifth root of a number is the number that would have to be multiplied by itself 5 times to get the original number.
For example, the fifth root of 243 is 3 as 3 x 3 x 3 x 3 x 3 is 243.
The fifth root of 1,024 is 4, as 4 x 4 x 4 x 4 x 4 is 1,024.
Formula – How to calculate the fifth root
Even for perfect fifth root numbers, the fifth root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the fifth root of 32,768
1) Try a number – 5 : 5 x 5 x 5 x 5 x 5 = 3,125 (too low)
2) Try another number that is more than 5 – 6 : 6 x 6 x 6 x 6 x 6 = 7,776(too low)
3) Try a number that is more than 6 – 10 – 10 x 10 x 10 x 10 x 10 = 100,000 (too high)
4) Try a number in between 6 and 10 – 8 – 8 x 8 x 8 x 8 x 8 = 32,768 (answer)
A fifth root can also be calculated as the same number to the exponent 1/5.
5√number = number1/5