# Seventh Root

LAST UPDATE: September 24th, 2020

## Definition – What is a seventh root?

The seventh root of a number is the number that would have to be multiplied by itself 7 times to get the original number.
For example, the seventh root of 2,187 is 3 as 3 x 3 x 3 x 3 x 3 x 3 x 3 is 2,187.
The seventh root of 16,384 is 4, as 4 x 4 x 4 x 4 x 4 x 4 x 4 is 16,384.

## Formula – How to calculate the seventh root

Even for perfect seventh root numbers, the seventh root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the seventh root of 2,097,152
1) Try a number – 5 : 5 x 5 x 5 x 5 x 5 x 5 x 5 = 78,125 (too low)
2) Try another number that is more than 5 – 6 : 6 x 6 x 6 x 6 x 6 x 6 x 6 = 279,936(too low)
3) Try a number that is more than 6 – 10 – 10 x 10 x 10 x 10 x 10 x 10 x 10 = 10,000,000 (too high)
4) Try a number in between 6 and 10 – 8 – 8 x 8 x 8 x 8 x 8 x 8 x 8 = 2,097,152(answer)
A seventh root can also be calculated as the same number to the exponent 1/7.
7√number = number1/7