First, not all square roots are irrational. For example, sqrt(9) has the perfectly rational solution of 3
Before we go on, let's review what it means to have an irrational number - it has to be a value that goes on forever in decimal form and is not a pattern, like pi. And since it has a never ending value that does not follow a pattern, it cannot be written as a fraction.
For example, 1/3 equals 0.33333333, but because it repeats we can write it a as fraction
Let's get back to your question. Some square roots, like sqrt(2) or sqrt(20 are irrational, since they cannot be simplified to a whole number like sqrt(25) can be. They go on forever without ever repeating, which means we can;t write it as a decimal without rounding and that we can't write it as a fraction for the same reason.
So, if a square root is not a perfect square, it is an irrational number
