Reboot loop while on battery only.

My tablet is almost 3 years old and has all latest updates installed. It has been working perfectly for the past few days. Yesterday, while on YouTube, it suddenly shut off (battery was on 45% charge). After that it quickly tried to reboot on it's own but as soon as it shows the Samsung logo, it again shuts off, again turns on to show logo and then off and this loop goes on. But when it was plugged to the charger, it shows that it's charging and then turns on and functions just as before.

What's going on with it? I really suspect a battery problem because I think it also charges irregularly when plugged (when unplugged, it again starts it's reboot loop) because it takes long to charge up, and when unplugged (of course, it shuts off then) and plugged again, it shows an entirely different battery percentage (like, 75% up from 48% a moment before).

In short, my tablet runs perfectly when plugged to the charger, but cannot run nor fully boot up when on the battery only and the charger unplugged (it starts the reboot loop when only on battery)

Should I replace the battery? Or might it be some other problem?

Great thanks for any help in advance :)