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Ninth Root Calculator

9th Root Calculator

What is a ninth root?

The ninth root of a number is the number that would have to be multiplied by itself 9 times to get the original number.
For example, the ninth root of 19,683 is 3 as 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 is 19,683.
The ninth root of 230,144 is 4, as 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 is 230,144.

How to calculate ninth root

Even for perfect ninth root numbers, ninth root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the ninth root of 134,217,728
1) Try a number – 5 : 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 1,953,125 (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 x 6 x 6 = 10,077,696 (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 x 10 x 10 = 1,000,000,000 (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 x 8 = 134,217,728 (answer)
An ninth root can also be calculated as the same number to the exponent 1/9.
9√number = number1/9

Table – Ninth Root (9√) of 1 – 100

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