  We theoretically present an economical and convenient way to study
ground-state properties of a strongly interacting superfluid Fermi gas. Our
strategy is that complicated strong-coupling calculations are used only to
evaluate quantum fluctuation corrections to the chemical potential $\mu$. Then,
without any further strong-coupling calculations, we calculate the
compressibility, sound velocity, internal energy, pressure, and Tan's contact,
from the calculated $\mu$ without loss of accuracy, by using exact
thermodynamic identities. Using a recent precise measurement of $\mu$ in a
superfluid $^6$Li Fermi gas, we show that an extended $T$-matrix approximation
(ETMA) is suitable for our purpose, especially in the BCS-unitary regime, where
our results indicate that many-body corrections are dominated by superfluid
fluctuations. Since precise determinations of physical quantities are not
always easy in cold Fermi gas physics, our approach would greatly reduce
experimental and theoretical efforts toward the understanding of ground-state
properties of this strongly interacting Fermi system.
