Just write it as 2^(1/12).

It evaluates as about 1.06.

The answer to this whimsical but useless exercise is "still infinity."

By convention, you cannot have a finite root of an indefinite number.

4,096

Examples of irrational numbers which are not square roots of whole numbers are pi (3.14159 to five decimal places), the golden ratio (1.6180339887...) and silver ratio (2.4142135623), and the twelfth root of two, which is the difference between any two notes in an even-tempered musical scale.

The twelfth day of January in the year two-thousand-twelve

-OR-

The twelfth day of January in the year two-thousand-and-twelve

-OR-

The twelfth day of the first month in the year two-thousand-twelve

-OR-

The twelfth day of the first month in the year two-thousand-and-twelve

And the such.