The motor uses 3kW. It might need more when it works hard.
If you make an inverter that has a 12V input and a 3kW 230V output then it wastes about 450W making heat. The battery must supply 3450W.
The 12V battery must supply 3450W/12V= 287.5A. That is rediculous unless you are towing a trailer full of huge batteries in parallel.
It will take weeks to charge that many batteries.
Rediculous.
The information provided by me and Audioguru already assumes power electronics to do the conversions.
Just remember that the power required has to be provided as the product of voltage and current: P=V*I. No amount of sophisticated circuitry can change this fact. If you use a low voltage source, you need high current. If you use a high voltage source, you need low current. Also, the conversion process wastes some power.