HOW CAN YOU TELL IF A SQUARE RoOT OF A NUMBER IS IN WHICH SET OF REAL NUMBERS?
The main way to tell is to know your definitions of these number categories. Natural numbers are counting numbers starting at 1, so if your radical is square root of 4, the answer is a natural number, 2. Whole numbers are all of the natural numbers and 0. Next, there are real numbers, which are all of the mentioned sets and also includes irrational and rational numbers, which are a little more tricky and probably the ones you want to distinguish between. The easiest way to tell the difference is to look at the decimal form of your number and if it is definite or has repeating terms, it is rational, but if it has no repeating terms it is irrational. Pi is the best known irrational number. Numbers like 4.5689 or 1.23232323… are rational numbers.
