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

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

• A. 2/3
• B. Sqrt(2)
• C. 4
• D. 0.5

Answer: (B)

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 \( \frac{p}{q} \), where \( p \) and \( q \) are integers and \( q \) is not zero. Irrational numbers have non-repeating and non-terminating decimal expansions. The square root of 2 is a well-known example of an irrational number. It cannot be precisely expressed as a fraction of two integers. In decimal form, \( \sqrt{2} \) is approximately 1.41421356..., and this decimal continues infinitely without repeating. Therefore, it qualifies as an irrational number. In contrast, the other options presented can be expressed as fractions. The fraction 2/3 is already in the form of a fraction, where both 2 and 3 are integers. The number 4 can also be expressed as the fraction \( \frac{4}{1} \), and 0.5 can be represented as \( \frac{1}{2} \). Since these numbers can be represented as fractions, they are classified as rational numbers. Thus, the square root of 2 stands out as the only irrational number among the choices

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{p}{q} ), where ( p ) and ( q ) are integers and ( q ) is not zero. Irrational numbers have non-repeating and non-terminating decimal expansions.

The square root of 2 is a well-known example of an irrational number. It cannot be precisely expressed as a fraction of two integers. In decimal form, ( \sqrt{2} ) is approximately 1.41421356..., and this decimal continues infinitely without repeating. Therefore, it qualifies as an irrational number.

In contrast, the other options presented can be expressed as fractions. The fraction 2/3 is already in the form of a fraction, where both 2 and 3 are integers. The number 4 can also be expressed as the fraction ( \frac{4}{1} ), and 0.5 can be represented as ( \frac{1}{2} ). Since these numbers can be represented as fractions, they are classified as rational numbers. Thus, the square root of 2 stands out as the only irrational number among the choices