To which set of real numbers does the following number belong?

√3

[] rational

[] irrational

[] whole

[] imaginary

Irrational would be the right answer!

Discussion

A whole number is a counting number. 2 5 29 44 18 are all counting numbers. They have no decimals trailing after them. C is not the answer.

An imaginary number is one like 18i where i is the square root of - 1. Nothing in our number system will give the square root of - 1 so we have to define that condition into our number system. i * i = - 1. So by definition and definition alone i is the square root of - 1. Those are called imaginary numbers because they are defined.

A rational number can be expressed as a fraction. It does not matter what kind of fraction. It is just a fraction. 3 1/3 = 10/3 That's a rational number. 14/7 is also rational.

sqrt (3) is irrational. It has an endless line of decimal places that have no pattern. 1/7 = 0.142857 ... repeating. But it is rational even though the decimal goes on forever. If I tell you the 70th place is a 5, I can tell you that the next digit will by a 7 [The 5 may not be true].

No such statement can be made about sqrt (3).

Answer: irrational.