To determine the nature of each number in the list (real, rational, irrational, integer, or whole number), we need to draw upon the definitions of these terms:
1. Real number: Any number that can be represented on the number line.
2. Rational number: Any number that can be expressed as a fraction (ratio) of two integers.
3. Irrational number: Any number that cannot be expressed as a fraction of two integers.
4. Integer: A number that can be either positive, negative, or zero, without a fractional or decimal part.
5. Whole number: A positive number that does not have a fractional or decimal part.
Now, let's analyze each number in the list:
1. Square root of 64: The square root of 64 is 8. This is a real number, a rational number, an integer, and a whole number because it can be expressed as the ratio of two integers (8/1) and is located exactly on the number line.
2. -5: -5 is a real number, a rational number, an integer, and not a whole number since it is negative. It can be expressed as the ratio -5/1 and is located on the number line.
3. Square root of 9: The square root of 9 is 3. This is a real number, a rational number, an integer, and a whole number because it can be expressed as the ratio of two integers (3/1) and is located on the number line.
4. 2: 2 is a real number, a rational number, an integer, and a whole number because it can be expressed as the ratio 2/1 and is located on the number line.
Now, let's order these numbers from least to greatest:
-5, 2, 3, 8
Therefore, the ordered list from least to greatest is -5, 2, 3, 8.
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