  We realize many sharp spectral bounds of the spectral radius of a nonnegative
square matrix $C$ by using the largest real eigenvalues of suitable matrices of
smaller sizes related to $C$ that are very easy to find. As applications, we
give a sharp upper bound of the spectral radius of $C$ expressed by the sum of
entries, the largest off-diagonal entry $f$ and the largest diagonal entry $d$
in $C$. We also give a new class of sharp lower bounds of the spectral radius
of $C$ expressed by the above $d$ and $f$, the least row-sum $r_n$ and the
$t$-th largest row-sum $r_t$ in $C$ satisfying $0<r_n-(n-t-1)f-d\leq
r_t-(n-t)f$, where $n$ is the size of $C$.
