  Let $x_1$ and $x_k$ be the least and the largest zeros of the Laguerre or
Jacobi polynomial of degree $k.$ We shall establish sharp inequalities of the
form $x_1 <A, x_k >B,$ which are uniform in all the parameters involved.
Together with inequalities in the opposite direction, recently obtained by the
author, this locates the extreme zeros of classical orthogonal polynomials with
the relative precision, roughly speaking, $O(k^{-2/3}).$
