Tell whether each number is a real number, rational number, irrational, interger, or whole number, and then order then from least to greatest.

( Square root sign) 49, 8, -( square root sign) 4, and -3.

Could someone explain to me how they found the answers to this?

To determine whether each number is a real number, rational number, irrational number, integer, or whole number, we need to understand the definitions of these terms.

1. Real numbers: Real numbers include all numbers on the number line, including rational and irrational numbers.
2. Rational numbers: Rational numbers are numbers that can be expressed as a fraction (the ratio of two integers), or as terminating or repeating decimals.
3. Irrational numbers: Irrational numbers are numbers that cannot be expressed as a fraction or as terminating or repeating decimals. Their decimal representations go on forever without repeating.
4. Integers: Integers include all whole numbers (positive, negative, or zero) and their opposites.
5. Whole numbers: Whole numbers include all positive integers (counting numbers) and zero.

Let's now determine the nature of each of the given numbers:

1. √49 (Square root of 49): This value equals 7, which is a whole number, integer, rational number (since it can be expressed as 7/1), and real number.

2. 8: This value is a whole number, integer, rational number (since it can be expressed as 8/1), and real number.

3. -√4 (Negative square root of 4): This value equals -2, which is a whole number, integer, rational number (since it can be expressed as -2/1), and real number.

4. -3: This value is an integer, rational number (since it can be expressed as -3/1), and real number.

Now, in order to order these numbers from least to greatest, we can arrange them as follows:

-3 < -√4 < 8 < √49

So, the order from least to greatest is: -3, -√4, 8, √49.

Note: Here, we are assuming that we are not looking for decimal approximations or exact values for irrational numbers.