Let us consider the expression $y = (\sqrt{x})^x$.

First, it's helpful to simplify or re-express it using properties of exponents and radicals:

The square root of $x$ can be written as $x^{1/2}$. So the expression becomes:

$y = (x^{1/2})^x.$

When raising a power to another power, you multiply the exponents. Thus:

$y = x^{x/2}.$

This expression represents $x$ raised to the power of $x/2$. If you need further analysis, such as finding the derivative or analyzing behavior for specific values of $x$, please let me know!