Which of the following is a rational number? Choices: (A)sqrt 10 (B)sqrt 8 (C)0 (D)𝜋

Define Rational Number: Define what a rational number is. 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. Evaluate sqrt(10): Evaluate each choice to determine if it is a rational number. Start with choice (A) sqrt(10). The square root of 10 is not a perfect square, and it cannot be expressed as a fraction of two integers. Therefore, sqrt(10) is an irrational number. Evaluate sqrt(8): Move on to choice (B) sqrt(8). The square root of 8 is not a perfect square, and it cannot be expressed as a fraction of two integers. Therefore, sqrt(8) is an irrational number. Consider 0: Consider choice (C) 0. The number 0 can be expressed as 0/1, where 0 and 1 are integers and 1 is not zero. Therefore, 0 is a rational number. Examine π: Finally, examine choice (D) π (pi). Pi is a well-known irrational number that cannot be expressed as a fraction of two integers. Therefore, π is an irrational number. Conclusion: Since we have found that choice (C) 0 is a rational number, and the other choices are not, we can conclude that the correct answer is (C) 0.

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Which of the following is a rational number? $\newline$ Choices: $\newline$ (A) $\sqrt{10}$ $\newline$ (B) $\sqrt{8}$ $\newline$ (C) $0$ $\newline$ (D) $\pi$

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Math Problems

Algebra 1

Domain and range of square root functions: equations

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Q. Which of the following is a rational number?

\newline

Choices:

\newline

(A)

\sqrt{10}

\newline

(B)

\sqrt{8}

\newline

(C)

0

\newline

(D)

\pi

Define Rational Number: Define what a rational number is. 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 $q$ is not zero.
Evaluate $\sqrt{10}$ : Evaluate each choice to determine if it is a rational number. Start with choice (A) $\sqrt{10}$ . The square root of $10$ is not a perfect square, and it cannot be expressed as a fraction of two integers. Therefore, $\sqrt{10}$ is an irrational number.
Evaluate $\sqrt{8}$ : Move on to choice (B) $\sqrt{8}$ . The square root of $8$ is not a perfect square, and it cannot be expressed as a fraction of two integers. Therefore, $\sqrt{8}$ is an irrational number.
Consider $0$ : Consider choice (C) $0$ . The number $0$ can be expressed as $0/1$ , where $0$ and $1$ are integers and $1$ is not zero. Therefore, $0$ is a rational number.
Examine $\pi$ : Finally, examine choice (D) $\pi$ (pi). Pi is a well-known irrational number that cannot be expressed as a fraction of two integers. Therefore, $\pi$ is an irrational number.
Conclusion: Since we have found that choice (C) $0$ is a rational number, and the other choices are not, we can conclude that the correct answer is (C) $0$ .