My aims 2000 pure sine wave inverter is pluged to 2 240amp/h 6 volt batteries. When | plug in a 1800 watt hairdrier i get an alarm as if the batt. were to low. they are new and at full charge. is the load to much for that size inverter?

Most likely your problem is in the battery type. You state that you have 2 240Ah batteries. I suspect these are deep discharge batteries which are designed to deliver low power over a long period of time. Typically the AmpHour (Ah) rating, for these type of batteries is stated at a 20 hour discharge rate. This would be a maximum of 10 amps per hour for 24 hours for the 240Ah batteries. However most batteries will only allow for a 75% efficiency so the actual delivered amperage will be about 7.5 amps per hour for 24 hours.
The wattage delivered at 7.5 dc amps at 12 v equals 90 watts. The inverter will deliver about 85% (efficiency of inverter) of this to the AC plug for about 75 watts. This is the optimum sustained load the battery will deliver for the stated 240 Ah capacity. Normally you would not drain the battery to this level. Typically battery manufacturers recommend not drawing the battery below 50% of its rated AmpHr capacity for maximum life.
As you begin to exceed the optimal wattage, particularly in a deep discharge battery, the efficiency of the battery drops, additional heat is generated, and voltage of the battery begins to drop. The higher the load the faster this occurs. I would expect in your situation (1800 watts 2-240Ah deep discharge batteries) to begin to get a low voltage alarm (about 11.5 volts) in less than a minute. You can verify this if your batteries are connected to an automotive alternator, as these can deliver high amperage as long as the engine runs. My RV has a 200 amp alternator, and when running will power 1500 watts through my alternator with no problem. Without the alternator running my Cobra 1575 inverter will shut down in about 30 seconds. (I have 2 225Ah deep discharge batteries that are new.)

Since you say the batteries are new and at full charge, the low voltage alarm is very likely due to the voltage drop in the cables between the batteries and inverter.

To reduce the so-called voltage drop**, you need to use as thick a set of cables as practical, kept as short as possible. Try again with thicker, shorter cables and you shouldn't hear the low voltage alarm. (With a 1800 watts load, those cable has to conduct around 150-160 amps of the ~12 volts DC current. That's a lot!)

**You can buy a cheap voltmeter/multimeter and measure the DC voltages at the inveter end and also at the battery terminals, while using the hair drier. The difference in voltage you observe is the voltage drop due to the inherent resistance in the cables. Thicker and shorter cables have less resistance, thus less voltage drop.

Your inverter has a peak of 3000 watts rating and should power that hair dryer. Make sure your batteries are in good shape. The inverter can only put out what it takes in. 1800 watt demand on the inverter requires 1800 watts from the batteries.

If you need further help, I’m available over the phone at https://www.6ya.com/expert/craig_3fa289bf857b1a3c