Concept of escape velocity-The minimum velocity with which a projectile should be projected from the surface of the earth is called as escape velocity.
It can be derived as follows.
Total energy of the projectile at infinity will be zero(at infinity means when project the projectile with a velocity v it will cross the gravitational field of the earth and escape to infinity. At infinity it will stop so its ke=0 and its gravitational potential=0. mind its gravitational potential not gravitational potential energy). so total energy of a system must remain constant therefore
1/2mv^2=Gmm/r
solving we get root under 2GM/R