Tell whether each number in the list is a real number, a rational number, an irrational number, an integer, or a whole number. Then order the numbers from least to greatest.
Square root of 64, -5, square root of 9, and 2
√64 is a whole number, an integer, a rational number as well as a real number
-5 is an integer, a rational number and a real number
√9 is a whole number, an integer, a rational number and a real number
2 is a whole number, an integer, a rational number and a real number
None of the numbers in your list are irrationals
To determine whether each number is a real number, a rational number, an irrational number, an integer, or a whole number, let's analyze each number one by one:
1. Square root of 64: The square root of 64 is 8. Since 8 is an integer, it is also a whole number and a rational number.
2. -5: -5 is an integer, and therefore it is also a whole number and a rational number.
3. Square root of 9: The square root of 9 is 3. Like the previous numbers, 3 is an integer, whole number, and rational number.
4. 2: 2 is an integer, whole number, and rational number.
To order the numbers from least to greatest, we can list them as follows:
-5, 2, 3, 8
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.