Question

Which of these numbers is an irrational number?

Answer 1

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). $\pi$ 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 $\sqrt{2}$. The $\sqrt{2}$ 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. 
$\frac{3}{5}$ 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.

$\frac{5}{3}$ 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 $\frac{2}{3}$ so that one is rational as well.

The correct answer would be the square root of 20.