Full solution

Q. Which of the following is an irrational number?

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Choices:

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(A)

\sqrt{5}

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(B)

\frac{1}{2}

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(C)

0

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(D)

8

Definition of Irrational Number: Understand the definition of an irrational number. An irrational number is a number that cannot be expressed as a simple fraction - that is, the ratio of two integers. It is a number that has a non-repeating, non-terminating decimal expansion.
Evaluate $\sqrt{5}$ : Evaluate option (A) $\sqrt{5}$ . $\newline$ The square root of $5$ is not a perfect square, which means it cannot be expressed as a simple fraction of two integers. Its decimal expansion is non-terminating and non-repeating. Therefore, $\sqrt{5}$ is an irrational number.
Evaluate $\frac{1}{2}$ : Evaluate option (B) $\frac{1}{2}$ . $\newline$ The number $\frac{1}{2}$ is a simple fraction and can be expressed as $0.5$ , which is a terminating decimal. Therefore, $\frac{1}{2}$ is not an irrational number.
Evaluate $0$ : Evaluate option (C) $0$ . The number $0$ can be expressed as the fraction $0/1$ , which is a simple fraction with a terminating decimal. Therefore, $0$ is not an irrational number.
Evaluate $8$ : Evaluate option (D) $8$ . The number $8$ is an integer and can be expressed as the fraction $\frac{8}{1}$ . It has a terminating decimal expansion. Therefore, $8$ is not an irrational number.
Select Correct Answer: Select the correct answer based on the evaluations. $\newline$ Since $\sqrt{5}$ is the only number among the options that cannot be expressed as a simple fraction and has a non-terminating, non-repeating decimal expansion, it is the only irrational number in the list.