Which choice is an example of an irrational number?

An irrational number is defined as a number that cannot be expressed as a simple fraction, meaning it cannot be written in the form of ( \frac{a}{b} ) where ( a ) and ( b ) are integers and ( b ) is not zero. Instead, the decimal representation of an irrational number goes on forever without repeating.

The choice of ( \sqrt{2} ) exemplifies this, as it cannot be written as a fraction of two integers. When calculated, the decimal approximation of ( \sqrt{2} ) is approximately 1.41421356..., and it continues indefinitely without a repeating pattern. This characteristic distinguishes it as an irrational number.

In contrast, the other choices can be expressed as fractions: ( \frac{1}{3} ) equals a repeating decimal (0.333...), 0.75 is equivalent to ( \frac{3}{4} ), and 7 can easily be represented as the fraction ( \frac{7}{1} ). Therefore, they are all classified as rational numbers.