What size inverter do I need?

Our Casita trailer has one Duracell AGM battery and a 100V Renogy portable solar panel. By 11 AM, the battery is typically 100% charged so we don't use all that much (I presume). Inside the RV, we use LED lights and other than that, the 3-way fridge and water pump use the RV battery, as well as us charging an iPad and cell phone by using the 12V outlet in the RV.

Now ... for charging my laptop while we're traveling, I bought a (cheap) 400W inverter at Walmart to plug into the RV's 12V outlet. Since the laptop charger is 90W, the solar panel barely keeps up while the laptop is charging during the day, but it works fine.

Question: I want to use my electric hair clipper, perhaps once every two weeks for 10 minutes, to keep my hair short. The hair clipper says on the back "120V AC 60Hz 8W".
When I plug it into the 400W inverter however, the blades don't move fast enough to cut my hair. It works but it hurts my head while cutting so I can tell it needs more 'power' to run faster as intended.
Can anyone tell me how big of an inverter I should get if 400W isn't enough?

Is it accurate to say that the hair clipper needs 120V and a 15-amp outlet so 120x15 = 1800W to run as intended and I only have 400W at the moment?

Thanks! (Yes, I'm challenged when it comes to electricity)

Jorn