Hi, there.
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First off, think about this: what is
?
If you do this on your calculator, you'll arrive at 2.449...
The key is:
is a number whose digits do not have any patterns. Whenever this happens the number's considered an irrational number.
Is it real? Reals are all numbers. The set of irrationals is a subset of reals. If a number's irrational it's also real.
It's not an integer. Irrationals are not a subset of the integers set.
It's not whole either.
√6 is only an irrational and a real number.
Hope the answer - and explanation - made sense,
happy studying.