This paper aims to find special cases of some inequalities for numerical radii and spectral radii of a bounded linear operator on a Hil-bert space, we focus on numerical radii inequalities for restricted linear operators on complex Hil-bert spaces for the case of one and two operators, and study the numerical range of an operator K on a complex Hil-bert space H, after that we present some inequalities for numerical radii and spectral radii and studied it to find new results. At the end of this paper we find several inequalities for numerical radii by using the spectral norm, this study is necessary to find other bound for zeros of polynomials and this study is necessary to find new bounds for the zeros of polynomials by a playing the new results to the companion matrix.