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Sixth Root Calculator

6th Root Calculator

What is a sixth root?

The sixth root of a number is the number that would have to be multiplied by itself 6 times to get the original number.
For example, the sixth root of 729 is 3 as 3 x 3 x 3 x 3 x 3 x 3 is 729.
The sixth root of 4,096 is 4, as 4 x 4 x 4 x 4 x 4 x 4 is 4,096.

How to calculate sixth root

Even for perfect sixth root numbers, sixth root can be difficult to calculate by hand.
The most basic techniques involve trial and error.
Example:
Find the sixth root of 262,144
1) Try a number – 5 : 5 x 5 x 5 x 5 x 5 x 5 = 163,840 (too low)
2) Try another number that is more than 5 – 6 : 6 x 6 x 6 x 6 x 6 x 6 = 46,656(too low)
3) Try a number that is more than 6 – 10 – 10 x 10 x 10 x 10 x 10 x 10 = 1,000,000 (too high)
4) Try a number in between 6 and 10 – 8 – 8 x 8 x 8 x 8 x 8 x 8 = 262,144 (answer)
A sixth root can also be calculated as the same number to the exponent 1/6.
6√number = number1/6

Table – Sixth Root (6√) of 1 – 100

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