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Tenth Root Calculator

10th Root Calculator

What is a tenth root?

The tenth root of a number is the number that would have to be multiplied by itself 10 times to get the original number.
For example, the tenth root of 59,049 is 3 as 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 x 3 is 59,049.
The ninth root of 690,432 is 4, as 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 is 690,432.

How to calculate tenth root

Even for perfect tenth root numbers, ninth root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the tenth root of 1,073,741,824
1) Try a number – 5 : 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 x 5 = 9,765,625 (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 x 6 = 60,466,176 (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 x 10 = 10,000,000,000 (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 x 8 = 1,073,741,824 (answer)
An ninth root can also be calculated as the same number to the exponent 1/10.
10√number = number1/10

Table – Tenth Root (10√) of 1 – 100

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