  We investigate the product form uncertainty relations of variances for
$n\,(n\geq 3)$ quantum observables. In particular, tight uncertainty relations
satisfied by three observables has been derived, which is shown to be better
than the ones derived from the strengthened Heisenberg and the generalized
Schr\"{o}dinger uncertainty relations, and some existing uncertainty relation
for three spin-half operators. Uncertainty relation of arbitrary number of
observables is also derived. As an example, the uncertainty relation satisfied
by the eight Gell-Mann matrices is presented.
