Let's first look at what an irrational number is. An irrational number is one that cannot be represented by whole numbers and/or fractions (also called ratios). 
is an irrational number because those decimals just go on and on and there is no pattern to be represented by a fraction. Many square roots are also irrational numbers as well, like 
. The is 1.414213... and cannot be changed into a fraction to represent all of those decimal places.
Now let's take a look at the answer choices you were given.
is written as a ratio (fraction), so that is a rational number.
The square root of 4 is 2 (2 x 2 = 4). This perfect square is also rational.
The square root of 25 is 5 (5 x 5 = 25). This one is also rational and a perfect square.
The square root of 20 is not a perfect square. There are no numbers we can multiply by themselves to get an answer of 20. If you were to put it into a calculator, you would get 4.472135955 - there's no pattern and no fraction this would convert to.
is an improper fraction that we can change to a mixed number. By dividing the denominator (3) into the numerator (5), you would get 1 with a remainder of 2. This would convert to a mixed number of 
so that one is rational as well.
The correct answer would be the square root of 20.
Now let's take a look at the answer choices you were given.
The square root of 4 is 2 (2 x 2 = 4). This perfect square is also rational.
The square root of 25 is 5 (5 x 5 = 25). This one is also rational and a perfect square.
The square root of 20 is not a perfect square. There are no numbers we can multiply by themselves to get an answer of 20. If you were to put it into a calculator, you would get 4.472135955 - there's no pattern and no fraction this would convert to.
The correct answer would be the square root of 20.