Question

Why are square roots irrational?

Answer 1

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