This paper uses some basic notions and results on the Laguerre hypergroup K = [0, +∞) × R to study some problems in the theory of approximation of functions in the space L 2 α (K). Analogues of the direct Jackson theorems of approximations for the modulus of smoothness (of arbitrary order) constructed by using the generalized translation operators on K are proved. The Nikolskii-Stechkin inequality is also obtained. In conclusion of this work, we show that the modulus of smoothness and the K-functionals constructed from the Sobolev-type space corresponding to the Laguerre operator L α are equivalent.