It looks really small for a turtle that size.
I've found that keeping turtles is somewhat like keeping fish. You have to have an appropriate size tank for not only space for the animal, but a big enough tank to support the biological needs. A turtle tank has to cycle just like an aquarium.
What this is is the nitrogen cycle. Your tank when started initially is literally too clean. There is no beneficial bacteria built up to help break down the waste the turtle produces. Water changes help dilute it, but they can only go so far. Cloudiness is generally due to an excess of waste/nutrients in the water. I'd have the water tested ASAP. Specifically you're looking for what the levels are of: ammonia, nitrites, and nitrates. Chances are, one of those is high which is causing the cloudy water.
Now, I know nothing about snappers so I may be off base in wondering about the water level in the tank. Personally, my two 1 1/2 yr old sliders have a 55 gallon (stand 4 foot variety) that is filled up within about 6 inches from the top of the tank. I noticed in your picture that yours was a rather low amount of water, likely indicating a tank too small for that size turtle.
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1.0.0 Thoroughbred
1.0.0 Mali Uromastyx
0.1.0 Bearded Dragon
0.1.0 Crested Gecko
1.2.0 German Shepherds
1.2.0 Cats
0.1.1 Birds (Cockatiel and Conure)
1.1.0 Rabbits
0.0.2 Yellow bellied sliders
3 Fish tanks (SW and FW)