To simplify \(3\) raised to the square root of \(64\), we start by calculating the square root of \(64\):
\[ \sqrt{64} = 8 \]
Now, we need to evaluate \(3^8\):
\[ 3^8 = 6561 \]
However, since the question seems to imply simplifying it down to an option, we'll clarify and ensure the original interpretation stands correct. The options given (16, 4, 8, 2) do not include \(6561\).
If we interpret further or retrace, we return and assume it asks beyond this scope, reaffirming calculations. Yet the math stays clear. The apparent misunderstanding could derive tasks within smaller exponentiation realms, yet the square root conditions encompass the root calculation, with \(3^8\).
Final answer determined is distinctly outside option reach, measured straightforward:
\( 3^{\sqrt{64}} = 3^8 = 6561 \), thus none of the options offers the fitment from this direct reduction, affirmed.
If options retain single-number simplifications, domain considerations or derived parsing might lead to substantive misinterpretation for immediate choices proposed.