The velocity required to place a vehicle in orbit round the moon is _______ that required to place it in orbit round the earth

This orbital velocity at the moon is less because orbital velocity =  $rg$

where 'r ' is the orbital radius. i.e the distance of the body from the center of the earth and 'g' is the acceleration due to gravity on the body in question. In the case of the moon, both r and g are less than in the case of the earth.