Before we consider the given number, let's recall the various types of numbers.

Rational Number: A number is a rational number if it can be written in the form $\frac{a}{b},$ where $a$ and $b$ are both integers and $b \neq = 0 .$
Integer: A number is an integer if it is a positive or negative counting number (or zero). All integers are also rational numbers because any number can be written as a division by one, $\frac{a}{1} .$

Whole Number: A number is a whole number if it is a non-negative counting number. All whole numbers are also integers and rational numbers.

Natural Number: A number is a natural number if it is a positive counting number. All natural numbers are also whole numbers, integers, and rational numbers.

Irrational Number: An irrational number is a number that cannot be written in the form of a rational number. These are recognized as being non-repeating, infinite decimals.

Now, let's try to categorize the given number using these definitions.

11

Because none of the factors of the radicand are perfect squares, this square root cannot be simplified. We can, however, use a calculator to find its exact value.

11 = 3.316624 \dots

Since the decimal part is infinite with non-repeating digits,

11

is an irrational number.

Exercise

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