A mixed identity in group G is an equation W(x)=1 where W is a non-trivial word in the free product G∗⟨x⟩. which is satisfied for all x∈G. Mixed Identity Free (MIF) means that no such identity holds on G. When G has no mixed identities, one wishes to find such x effectively (w.r.t the word metric). Set f(n)=min { | g | : g∈G , W(g)≠1 for all W∈B(n) } where B(n) is the n-th ball in G∗⟨x⟩. If f is sub-exponential there are interesting applications for the reduced C*-algebra of the group, especially when the group also has rapid decay. Recently, Elayavalli and Schafhauser gave a negative answer for the C*-algebraic Tarski problem by studying this property for free groups. More recently, Itamar Vigdorovich extended their work to uniform lattices in SL(n,R). What we proved is: Theorem 1. For a f.g. linear group \Gamma with MIF, the function f is linear (i.e. f(n)<Cn). If the Zariski closure G is a classical group, then \Gamma is MIF, provided G is PSL(n), or G=SP_{2r} and \Gamma has no elements of order 2, or G=SO(n) and \Gamma has no elements g for which g+g^{-1} is a scalar. Along the way, we proved a new variant of the supper approximation theorem, which is of independent interest. This is a joint work with Nir Avni.