Sure, let's explore the numerical classification of each of these numbers one by one:
1. √121: The square root of 121 is 11. Notice that 11 is a complete unit without any fractional or decimal components. Thus, we categorize 11 as a whole number. It can also fit into the Integer category since integers include all whole numbers, both negative and positive. Lastly, it is a Rational number because you can express it as a fraction where 11 is the numerator and 1 is the denominator. Hence, √121 is a whole number, an Integer, and a Rational number.
2. 56: The number 56 is a whole number because it does not have any fractional or decimal component. It is also an Integer number because integers include every whole number, whether it is positive, negative or zero. Moreover, it is a Rational number because you can express it as a fraction where 56 is the numerator and 1 is the denominator. Therefore, 56 is a whole number, an Integer, and a Rational number.
3. 3.6666666666: This number, as you can see, is a fraction in decimal form. Furthermore, it has a non-repeating decimal fraction which does not terminate. Since the decimals here do not form a repeating pattern, we call this type of number an Irrational number. Consequently, 3.6666666666 is an Irrational number.
4. 1/4: This one is clearly a fraction. Since it's possible to express all fractions as a division of two integers (where the denominator isn't zero), we classify them as Rational numbers. Here, you can express 1/4 as 0.25 in decimal form which clearly shows it as a Rational number. Hence, 1/4 is a Rational number.
So, √121 and 56 are classified as whole numbers, integers, and rational numbers. 3.6666666666 is an irrational number and 1/4 is a rational number.
Answer: D. Rational