Which of the following is a rational number? Choices: (A)sqrt 5 (B)𝜋 (C)sqrt 6 (D)6.333...

Definition of Rational Number: A rational number is a number that can be expressed as the quotient or fraction p/q of two integers, where p and q are integers and q is not zero. Let's examine each choice to determine if it is a rational number.Choice (A): sqrt(5): Choice (A) is sqrt(5). The square root of 5 is an irrational number because it cannot be expressed as a fraction of two integers. It is a non-repeating, non-terminating decimal.Choice (B): π (pi): Choice (B) is π (pi). Pi is a well-known irrational number. It is a non-repeating, non-terminating decimal and cannot be expressed as a fraction of two integers.Choice (C): sqrt(6): Choice (C) is sqrt(6). The square root of 6, like the square root of 5, is an irrational number because it cannot be expressed as a fraction of two integers. It is also a non-repeating, non-terminating decimal.Choice (D): 6.333...: Choice (D) is 6.333... Since the number 6.333... has a repeating decimal, it can be expressed as a fraction. In this case, the repeating decimal 0.333... is equivalent to 1/3, so 6.333... is equivalent to 6 + 1/3, which can be written as 19/3, a fraction of two integers.

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Which of the following is a rational number? $\newline$ Choices: $\newline$ (A) $\sqrt{5}$ $\newline$ (B) $\pi$ $\newline$ (C) $\sqrt{6}$ $\newline$ (D) $6.333\ldots$

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Algebra 2

Simplify radical expressions with root inside the root

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Q. Which of the following is a rational number?

\newline

Choices:

\newline

(A)

\sqrt{5}

\newline

(B)

\pi

\newline

(C)

\sqrt{6}

\newline

(D)

6.333\ldots

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 $p$ and $q$ are integers and $q \neq 0$ . Let's examine each choice to determine if it is a rational number.
Choice (A): $\sqrt{5}$ : Choice (A) is $\sqrt{5}$ . The square root of $5$ is an irrational number because it cannot be expressed as a fraction of two integers. It is a non-repeating, non-terminating decimal.
Choice (B): $\pi$ (pi): Choice (B) is $\pi$ (pi). Pi is a well-known irrational number. It is a non-repeating, non-terminating decimal and cannot be expressed as a fraction of two integers.
Choice (C): $\sqrt{6}$ : Choice (C) is $\sqrt{6}$ . The square root of $6$ , like the square root of $5$ , is an irrational number because it cannot be expressed as a fraction of two integers. It is also a non-repeating, non-terminating decimal.
Choice (D): $6.333\ldots$ : Choice (D) is $6.333\ldots$ Since the number $6.333\ldots$ has a repeating decimal, it can be expressed as a fraction. In this case, the repeating decimal $0.333\ldots$ is equivalent to $\frac{1}{3}$ , so $6.333\ldots$ is equivalent to $6 + \frac{1}{3}$ , which can be written as $\frac{19}{3}$ , a fraction of two integers.