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nth Root Calculator

nth Root Calculator

root
3

What is a nth root?

The nth root of a number is the number that would have to be multiplied by itself n times to get the original number.
For example, the 3rd root of 27 is 3 as 3 x 3 x 3 is 27.
The 5th root of 1,024 is 4, as 4 x 4 x 4 x 4 x 4 is 1,204.

How to calculate nth root

Even for perfect nth root numbers, a 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)
Example 2:
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 fourth root can also be calculated as the same number to the exponent 1/4.
4√number = number1/4

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