Failed to escape 'n caught by the Moon

Imagine, for now, the Sun 'n the Venus and the Mars 'n the Uranus, all have gone. What's left behind is our Earth 'n Moon. And they have gone stationary.

As you see here, the mass of earth $M_{e}=5.972*10^{24} kg$ and the mass of the moon is $M_{m}=7.348*10^{22} kg$ . And the distance between them ( Center 2 Center ) measures $d=3.84*10^{8}m$ , as it should be. But you know, something must change, the radius of the earth became $R_{e}=6.4*10^{7}m$ but the radius of the moon is, as usual, $R_{m}=1.37*10^{6}m$ .

Now we wanna send a rocket from the earth's surface $A$ , and then we want it to land on the moon surface $B$ . Calculate the least velocity ( in $ms^{-1}$ ) it must be given.

Assume the rocket to be a point object and that it travels along the line joining the centers of the planets.

Given : $G=6.673*10^{-11} Nm^{2}kg^{-2}$

HInt: The answer isn't 1801, it's more...