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

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

• A. 1/2
• B. 0.3333...
• C. √5
• D. 7

Answer: (C)

An irrational number is defined as a number that cannot be expressed as a simple fraction or a ratio of two integers. This means that its decimal representation is non-terminating and non-repeating. The square root of 5 is an example of an irrational number. This is because it cannot be simplified to a fraction. Its decimal form is approximately 2.236067977..., continuing infinitely without repeating. Therefore, √5 meets the criteria for being classified as irrational. In contrast, the other options represent numbers that can be expressed as fractions. The fraction 1/2 is a rational number because it can be explicitly represented as a ratio of integers. The number 0.3333..., while it has a non-terminating decimal form, is a repeating decimal and can be expressed as the fraction 1/3, hence it is rational. The whole number 7 can also be expressed as a fraction (7/1), making it rational as well. Thus, the choice of √5 clearly aligns with the definition of an irrational number, making it the correct answer.

An irrational number is defined as a number that cannot be expressed as a simple fraction or a ratio of two integers. This means that its decimal representation is non-terminating and non-repeating.

The square root of 5 is an example of an irrational number. This is because it cannot be simplified to a fraction. Its decimal form is approximately 2.236067977..., continuing infinitely without repeating. Therefore, √5 meets the criteria for being classified as irrational.

In contrast, the other options represent numbers that can be expressed as fractions. The fraction 1/2 is a rational number because it can be explicitly represented as a ratio of integers. The number 0.3333..., while it has a non-terminating decimal form, is a repeating decimal and can be expressed as the fraction 1/3, hence it is rational. The whole number 7 can also be expressed as a fraction (7/1), making it rational as well.

Thus, the choice of √5 clearly aligns with the definition of an irrational number, making it the correct answer.