How many days does rocket takes to reach the moon from Earth?
Moon is not that close to Earth as we think of it.
Fun fact: You can fit all the remaining planets of the solar system in the space between the Earth and the Moon.
Now that you have an idea how far it really is, let’s answer your question. There is no fixed time in which a rocket can reach from Earth to the Moon.
You have to keep in mind a lot of things before doing this.
The location from where the rocket is being launched from Earth. Assuming the direction of launch towards East direction as all rockets do so. Relative position of Moon at the time of launch with Earth. As the moon orbits earth in an elliptical orbit, so sometimes it is closer to us. Budget of the mission, this will be most crucial, because-If you are having no money constraints, you can build up a hell of a powerful rocket that will cut off time to reach there. For budget missions, various fuel saving techniques are used like slingshot the payload using Earth’s gravity towards the Moon. It is a more time consuming approach but drastically reduces mission cost.
Considering all the above options, you may reach there quite fast, say in about 9 hours like the New Horizon Probe, which flied past the moon on it’s way to Pluto or you can have a slower approach taking upto a few days like the Appolo missions.