Which of the following is an irrational number?

An irrational number is defined as a number that cannot be expressed as a fraction of two integers, meaning it cannot be written in the form ( \frac{a}{b} ), where ( a ) and ( b ) are integers, and ( b ) is not zero. Instead, irrational numbers have non-repeating, non-terminating decimal expansions.

The square root of 2 is a classic example of an irrational number. Its decimal expansion is approximately 1.41421356... and continues on without repeating. There are no two integers that can combine to form this value as a fraction, confirming it as irrational.

On the other hand, the other numbers provided—1, 2, and 3—are all integers and can be expressed as fractions (for instance, ( 1 = \frac{1}{1} ), ( 2 = \frac{2}{1} ), and ( 3 = \frac{3}{1} )). Since they can be written this way, they are classified as rational numbers. Thus, the square root of 2 stands out as the only irrational number in the list.