You all, hopefully, realise this was an ill defined problem. It is presented as Euclidean, and solved in the Argand realm. You have learned about the "bait and switch" technique. Both answers are correct, depending on your starting point,

Not Clearly understand may use ALGEBRA form

Catalan 's conjuncture (a^x) & (b^y) are consucative ; a,b,x,y≥2 => a^x,b^y = 8,9

Al-Jabra » Algebra 9th Century's Arabic Word

Bezout's Identity gcd(a,b) = ax + by ; x,y∈N

So its x^x?

Underated

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Lengths can only be positive integers and irrational numbers as length can never be negative or imaginary as it is a real life magnitude