Summary: We consider the one-dimensional squared Bessel process given by the stochastic differential equation (SDE) \[ \mathrm dX_t = 1\mathrm dt + 2 \sqrt{X_t} \mathrm{d}W_t, \qquad X_0 = x_0, \qquad t \in [0,1], \] and study strong (pathwise) approximation of the solution \(X\) at the final time point \(t=1\). This SDE is a particular instance of a Cox-Ingersoll-Ross (CIR) process where the boundary point zero is accessible. We consider numerical methods that have access to values of the driving Brownian motion \(W\) at a finite number of time points. We show that the polynomial convergence rate of the \(n\)-th minimal errors for the class of adaptive algorithms as well as for the class of algorithms that rely on equidistant grids are equal to infinity and \(1/2\), respectively. This shows that adaption results in a tremendously improved convergence rate. As a by-product, we obtain that the parameters appearing in the CIR process affect the convergence rate of strong approximation.