A rational number is a number that can be expressed in the form p/q. in this case p=3 and q=1. The other answers are irrational because they cannot be expressed as whole numbers or fractions.

Step 1: Define the different sets:

Rational: Any number that can be expressed as a fraction (improper/proper form) (example: )
Irrational: Any number whose decimal expansion cannot be written as a fraction. (example: )
Real numbers: The combination of all numbers that belong in the Rational and the Irrational set.  (Example: )
Integers: All whole numbers from . (Example: )
Natural Numbers (AKA Counting numbers): All numbers greater than or equal to 1, 

Step 2: Let's categorize the numbers given in the question to these sets above:

 belongs to the set of rational numbers, natural numbers, and integers.
 belongs to the set of rational numbers and integers.
 belongs to the set of rational numbers.

Step 3: Analyze each number closely and pull out any sets where all three numbers belong..

All three numbers belong to the set of rational numbers.

In math, we symbolize rational numbers as .
So, all three numbers belong to the sets .

The definition of natural numbers states that the number may not be negative, and must be countable where:

Decimal places and fractions are also not allowed.

The value of fifty percent equates to .

The only possible answer is:  

Natural numbers are numbers can be countable.  Natural numbers cannot be negative.  They are whole numbers which include zero.

The fraction given is not a natural number.

Notice that the imaginary term  can be reduced.  Recall that , and .  This means that .

The answer is:  

A rational number, by definition, is one that can be expressed as a quotient of integers. Each of the fractions in the set -  - is such a number. The sole integer, 1, is also rational, since any integer can be expressed as the quotient of the integer itself and 1.

The whole numbers are defined to be 0 and the so-called counting numbers, or natural numbers 1, 2, 3, and so forth. Negative integers  and  are not included in this set.

By definition, a complex number is a number with an imaginary term denoted as i.

A complex number is in the form,

where  represents the real part of the number and  represents the imaginary portion of the complex number.

Therefore, the complex number which is the solution is .

By the Quotient of Powers Property,

.

Therefore, each element, the square root of a fraction, can be seen to be the fraction of the square roots of the individual parts. Each numerator and denominator is a perfect square, so each square root is a fraction of integers:

By definition, any integer fraction, being a quotient of integers, is a rational number, so all elements in the set are rational.

To raise  to the power of any positive integer, divide the integer by 4 and note the remainder. The correct power is given according to the table below.

Every element in the set is equal to  raised to an even-numbered power, so when each exponent is divided by 4, the remainder will be either 0 or 2. Therefore, each element is equal to either 1 or . Consequently, the set includes no imaginary numbers.

An irrational number is any number that cannot be written as a fraction of whole numbers.  The number pi and square roots of non-perfect squares are examples of irrational numbers.  

 can be written as the fraction .  The term  is a whole number.  The square root of  is , also a rational number. , however, is not a perfect square, and its square root, therefore, is irrational.