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$O(nlog(√n))$ and $O(nlog(n))$ belongs to same class of function with respect to Big O notation. There is no difference between them other than a constant factor.
$\lim_{x\to\infty} (nlog(√n)) / (nlog(n))$ = $\lim_{x\to\infty} 1/2*(nlog(n))/(nlog(n))$ = $1/2$