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Which of the following are rational numbers? $\newline$ Multi-select Choices: $\newline$ (A) $\frac{5}{7}$ $\newline$ (B) $\frac{2}{7}$ $\newline$ (C) $\sqrt{8}$ $\newline$ (D) $0$

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Full solution

Q. Which of the following are rational numbers?

\newline

Multi-select Choices:

\newline

(A)

\frac{5}{7}

\newline

(B)

\frac{2}{7}

\newline

(C)

\sqrt{8}

\newline

(D)

0

Definition of Rational Number: A rational number is a number that can be expressed as the quotient or fraction $\frac{p}{q}$ of two integers, where $p$ is the numerator, $q$ is the denominator, and $q \neq 0$ . We will check each option to see if it meets this definition.
Option (A) Analysis: Option (A) is $\frac{5}{7}$ . Since both $5$ and $7$ are integers and $7$ is not zero, $\frac{5}{7}$ is a fraction of two integers where the denominator is not zero. Therefore, $\frac{5}{7}$ is a rational number.
Option (B) Analysis: Option (B) is $\frac{2}{7}$ . Similar to option (A), $\frac{2}{7}$ is a fraction of two integers where the denominator is not zero. Therefore, $\frac{2}{7}$ is also a rational number.
Option (C) Analysis: Option (C) is $\sqrt{8}$ . The square root of $8$ is not a rational number because it cannot be expressed as a fraction of two integers. The square root of $8$ is an irrational number because it is a non-repeating, non-terminating decimal.
Option (D) Analysis: Option (D) is $0$ . Zero is a rational number because it can be expressed as $\frac{0}{1}$ , or the fraction of two integers where the denominator is not zero.

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