Which of the following numbers is irrational? negative 15 over 4, negative 7 over 9, square root of 4, π negative 15 over 4 negative 7 over 9 square root of 4 π,

An irrational number is one that can’t be expressed as a simple fraction.

For instance, the first few digits of the square root of two is written as 1.414213562373095... The digits keep going and cannot be expressed as a fraction. But think of 0.33333... That can easily be written as one-third. The distinguishing feature is that there’s no pattern in the digits for the square root of two.

The first two options are integer fractions. We rule those out immediately. The square root of four is tempting, but realize that it is just equal to two. We come to π (pi).

Arguably the most famous irrational number is π, which starts off as 3.14159265358979... Here, there is again no pattern and the digits extend forever. This meets our definition of our irrational.