square root of (2 or 3 or 5 or 6 or 7 or 8 etc.)
pi
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'pi' and 'e' both fit that description.
To 4.5, add the difference between the two numbers (0.1), multiplied by some irrational number that is less than 1 (or divided by an irrational number greater than 1). For example:4.5 + 0.1 / pi
You can choose an irrational number to be either greater or smaller than any given rational number. On the other hand, if you mean which set is greater: the set of irrational numbers is greater. The set of rational numbers is countable infinite (beth-0); the set of irrational numbers is uncountable infinite (more specifically, beth-1 - there are larger uncountable numbers as well).
A prime number is a natural number that has no natural number as a factor other than itself or 1. An irrational number is not a natural number, so an irrational number can't be prime.
No, numbers less than 0.833 are not always irrational. For instance, 0.2 isn't an irrational number