From the positivity of 2×2 block matrices, we study the Schatten p-norm inequalities for the sum and product of n×n complex matrices via the singular values and the Moore-Penrose inverses. Using these inequalities, we deduce the p-numerical radius and the classical numerical radius bounds. We also study the Euclidean operator radius inequalities for a pair of bounded linear operators via the Moore-Penrose inverse, and we deduce new classical numerical radius bounds.