I am assuming that, n is a prime number, because you can express composite numbers to prime by enlarging the exponent.
a = nn^x-1 = n
I don't know how to prove or disprove it, but if x is odd then,
a is always multiplied by a prime number, which square rooted are irrational.
For example n=5; x=11
√5^11 = √5^105 = 5^5√5
The prime number is left in the sqrt.
Is my hint correct? I don't think it completely proves this theory.
If x is even, then halving the exponent is good enough.
N and x values are acceptable as disproving.
Thanks.