The geometric-arithmetic index $GA$ of a graph $G$ is the sum of ratios, over all edges of $G$, of the geometric mean to the arithmetic mean of the end vertices degrees of an edge. The spectral radius $\lambda_1$ of $G$ is the largest eigenvalue of its adjacency matrix. These two parameters are known to be used as molecular descriptors in chemical graph theory.
In the present paper, we compare $GA$ and $\lambda_1$ of a connected graph with given order. We prove, among other results, upper and lower bounds on the ratio $GA/\lambda_1$ as well as a lower bound on the ratio $GA/\lambda_1^2$. In addition, we characterize all extremal graphs corresponding to each of these bounds.