Let us know which monitor you are thinking about getting too if you want us to help check, but the G750JM user manual shows your G750JM notebook has a variety of ports that you can use for external monitors as below.
1. Mini Display Port
2. HDMI Port
3. VGA Port
Your monitor is probably using at least one of these ports although you want to avoid using the 'VGA' Port if possible which will have lower quality, but for some older monitors and projectors that may be your only option, so it's still better than nothing.
Your monitor might even include the cables if you want to look into this, but the right cable should not be too difficult to find if you need to get one.
Note: If you decide you want to use the Display Port input on your monitor if available, you will probably need some kind of mini Display Port to Display Port adapter or cable to connect your G750JM to to your new monitor.
Note #2: Some monitors may also use a 'DVI Input' and you would need to get some kind of hdmi to DVI adapter or cable to connect to the monitor this way.
Feel free to discuss and it's something your local ASUS Support should be able to discuss too if you're interested.
http://www.asus.com/support/callusHope this helps.