Which of the following numbers is an example of an irrational number?

An irrational number is defined as a number that cannot be expressed as a simple fraction 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 (√2) is a classic example of an irrational number. It cannot be precisely expressed as a fraction, and when computed, its decimal form begins as 1.41421356... and continues indefinitely without repeating. This property of having an infinite, non-repeating decimal expansion is what categorizes √2 as irrational.

In contrast, the other numbers listed can be expressed in fractional form or have finite decimal representations. For instance, 0.75 is a terminating decimal and can be written as the fraction 3/4. Similarly, 1/3 is a repeating decimal (0.333…) but still a rational number because it can be expressed as the fraction itself. The number 7 is also a whole number and can be represented as 7/1, making it rational as well. Therefore, among the given options, √2 stands out as the only number that is not rational, firmly placing it in the category of irrational numbers.