Q. Which of the following is a rational number?Choices:(A) 72β(B) Ο(C) 3β(D) 8β
Definition of Rational Number: A rational number is a number that can be expressed as the quotient or fractionqpβ of two integers, where p and q are integers and q is not zero. We will examine each choice to determine if it can be expressed in this form.
Choice (A): 72β: Choice (A) is 72β. This is already in the form of a fraction where both the numerator (2) and the denominator (7) are integers, and the denominator is not zero. Therefore, 72β is a rational number.
Choice (B): Ο: Choice (B) is Ο (pi). Pi is a transcendental number, which means it cannot be expressed as a fraction of two integers. Therefore, Ο is not a rational number.
Choice (C): 3β: Choice (C) is the square root of 3. The square root of 3 is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal expansion is non-terminating and non-repeating. Therefore, 3β is not a rational number.
Choice (D): 8β: Choice (D) is the square root of 8. The square root of 8 simplifies to 2 times the square root of 2, which is an irrational number. Therefore, 8β is not a rational number.
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