The Randi\' c index of a graph $G$ is defined as the sum of weights $1/\sqrt{d_ud_v}$ over all edges $uv$ of $G$, where $d_u$ and $d_v$ are the degrees of the vertices $u$ and $v$ in $G$, respectively. In this paper, we will obtain lower and upper bounds for the Randi\' c index in terms of size, maximum degree, and minimum degree. Moreover, we obtain a generally lower and a general upper bound for the Randi\' c index.
