Let T be a bounded linear operator on a complex Hilbert space H. We obtain various lower and upper bounds for the numerical radius of T by developing the Euclidean operator radius bounds of a pair of operators, which are stronger than the existing ones. In particular, we develop an inequality that improves on the inequality Various equality conditions of the existing numerical radius inequalities are also provided. Further, we study the numerical radius inequalities of 2 × 2 off-diagonal operator matrices. Applying the numerical radius bounds of operator matrices, we develop upper bounds of w(T) by using t -Aluthge transform. In particular, we improve the well known inequality where T = |T|1/2|U|T|1/2 is the Aluthge transform of T and T = U|T| is the polar decomposition of T.