If I know that a^6 = 1,771,56, how do I find a?

You could first take the square root of the number, then take the cube root of that.

 

Or you could use a calculator that allows you to take any power, here you'll take the number to the power 0.16666667  because that is the decimal value of 1/6, at least approximately.

 

Or you could use logarithms.

 

BTW, your number has the commas in the wrong places, or maybe there's a digit has gone missing?  🐾

Pull the 6th root 6:

 

sqrt6(1.7715690000000003301)