Final answer:
The square root of 36/9 simplifies to the whole number 2, which belongs to the sets of natural numbers, whole numbers, integers, and rational numbers.
Step-by-step explanation:
To determine which set or sets the number square root of 36/9 belongs to, we first need to perform the given operation. The square root of 36 is 6, and 6 divided by 9 is two-thirds. However, two-thirds can be further simplified to the whole number 2 because 6 divided by 9 simplifies to 6/9 which is equivalent to 2/3, and 2/3 of 3 is indeed 2. Therefore, the number we are evaluating is simply 2.
A Whole number is a number without fractions; an integer that is 0 or positive. Hence, our number 2 fits into this category. Since all whole numbers are also integers and natural numbers, 2 belongs to these sets as well. By definition, an integer is a whole number that can be positive, negative, or zero. A natural number is a positive integer used for counting and ordering. Lastly, a rational number is any number that can be expressed as the quotient or fraction of two integers. Therefore, 2 is also a rational number because it can be written as 2/1.