The [square root of 10] is 3.16 which isn't a natural number but a rational number instead?

A

*natural number* is some whole number (not a fraction) that is not negative and, depending on who you ask, may include zero. The square root of 10 is positive, but it falls between 3 and 4. It is not a whole number, and therefore is not a natural number.

The square root of 10 has more digits than just those three. It's actually 3.16227766016837933... well, I can't type them all out here because they just keep going forever and ever, and they ultimately do not repeat.

Any whole number, including the natural numbers and negative whole numbers, is known as an

*integer*.

A number that can be expressed as a division of integers is called a

*rational number* (which includes the integers and all fractions). Sometimes these make short and simple figures in decimal form, but sometimes they go on forever. However, if a fraction does go on forever in decimal form, then the sequence of digits is guaranteed to repeat after a certain point.

Otherwise, if a number is not a whole number and the digits never repeat, that's what's called an

*irrational number*. It happens to be that, for any natural number that is not itself the square of a natural number, its square root will always be irrational.