The number of ways to select three elements from a set of eight is the number of combinations of three elements chosen from eight:

20 can be factored as:

I) 

II) 

III) 

The positive difference of the factors can be any of:

Of the four choices, only 8 is possible.

 is a well-known irrational number and is not the correct choice. 

. The square root of an integer is rational only if it is itself an integer; calculation yields a result of 1.414... This is not the correct choice.

, since . This is an integer and is not the correct choice.

, so, by definition, . This is rational and is therefore the correct choice.

, which is not an integer. It is not a whole number either, as the whole numbers consist of all (nonnegative) integers.

. As the quotient of integers, it is rational. 

Therefore,  belongs to the set of rational numbers but not to the other two sets. The correct response is one.

A number in base sixteen has powers of sixteen as its place values; starting at the right, they are .

The lowest base sixteen number with three digits would be

 in base ten.

The lowest base sixteen number with four digits would be

 in base ten.

Therefore, a number that is expressed as a three-digit number in base sixteen must fall in the range

.

Of the four numbers listed, 1,000 falls in that range.

The set of whole numbers comprises 0 and the so-called natural, or counting, numbers; that is, it is the set .  is not one of these numbers.

The set of integers comprises these numbers as well as their (negative) opposites; that is, it is the set .  is one of these numbers.

A prime number is a positive integer which has exactly two factors - 1 and the number itself. 36, 38, and 39 can each be shown to have at least one other factor:

, so 2 and 18 are factors of 36, making 36 not prime.

, so 2 and 19 are factors of 38, making 38 not prime.

, so 3 and 13 are factors of 39, making 39 not prime.

37, however, cannot be evenly divided by any number except for 1 and itself, as can be seen below:

We do not need to go higher, since any higher possible factors have square greater than 37. 37 has been proved a prime number.

An integer is an element of the set of numbers 

that is, the so-called natural, or "counting", numbers, their (negative) opposites, and 0. , 2, , and 1 are elements of this set; and are not. The correct response is 4.

Remember that a complex number is any number that includes  or .

 is irrational but real.  

Similarly,  which is irrational but real.

A prime number is a number that is evenly divisible by , the number itself, and no other number. 

 is the only number that is not evenly divisible by a number other than  and the number itself.