Is the square root of 32 an irrational or a rational number?

The square root of a positive integer can ONLY be:* Either an integer,

* Or an irrational number.

(The proof of this is basically the same as the proof, in high school algebra books, that the square root of 2 is irrational.)

Since in this case 32 is not the square of an integer, it therefore follows that its square root is an irrational number.