Which of the following is a rational number?
√2.56 is a rational number.
The square root of 2.56 equals 1.6, which can be expressed as the fraction 16/10 or 8/5, thus confirming that it is a rational number. A rational number is defined as any number that can be expressed as the quotient of two integers, and since 1.6 meets this criterion, it qualifies as rational.
This option is the correct choice, as the square root of 2.56 equals 1.6, which is a rational number. It can be expressed as a fraction (16/10 or 8/5), satisfying the definition of rationality.
The square root of 10.0 is approximately 3.162, an irrational number. It cannot be expressed as a fraction of two integers, as it has a non-repeating, non-terminating decimal expansion. Therefore, it does not meet the criteria for being a rational number.
The square root of 28.9 is approximately 5.385, which is also an irrational number. Similar to option B, it cannot be expressed as a fraction of integers because it has a decimal expansion that does not terminate or repeat, disqualifying it from being rational.
The square root of 32.4 is roughly 5.7, which is yet another irrational number. Its decimal representation does not terminate or repeat, making it impossible to express as a fraction of two integers, hence it cannot be classified as a rational number.
In summary, among the given options, only √2.56 qualifies as a rational number, as it can be expressed as a fraction. The other choices—√10.0, √28.9, and √32.4—are irrational numbers due to their non-terminating and non-repeating decimal forms, which do not meet the criteria for rationality.
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