The number √13 can be classified as follows:
- Irrational Number: It cannot be expressed as a fraction of two integers, and its decimal representation is non-repeating and non-terminating.
- Real Number: All irrational numbers are real numbers.
The other classifications do not apply to √13:
- Rational Number: False, as it cannot be expressed as a fraction of two integers.
- Whole Number: False, as it is not a non-negative integer.
- Natural Number: False, as it is not a counting number.
- Integer: False, as it is not a whole number.
- Repeating Decimal: False, as its decimal representation is non-repeating.
- Terminating Decimal: False, as it does not end.
- Non-repeating Decimal: True, √13 is a non-repeating decimal.
- Non-terminating Decimal: True, √13 is a non-terminating decimal.
So, the applicable classifications for √13 are:
- Irrational Number
- Real Number
- Non-repeating Decimal
- Non-terminating Decimal