18. Which of the following is a rational number?
Answer: A
√2.56 is a rational number.
The number √2.56 can be expressed as a fraction, specifically 1.6, making it a rational number. Rational numbers are defined as numbers that can be expressed as the quotient of two integers.
A) √2.56
This option is correct because √2.56 equals 1.6, which can be represented as the fraction 8/5. Since it can be expressed in the form of a/b where a and b are integers, it is classified as a rational number.
B) √10.0
This option is incorrect because √10.0 equals √10, which is an irrational number. It cannot be expressed as a fraction of two integers, making it a non-rational number.
C) √28.9
This option is incorrect as well since √28.9 equals 5.375, which can be expressed as the fraction 43/8. However, this is not the case here, as the main emphasis is on the irrational nature of the square root of non-perfect squares like 28.9.
D) √32.4
This option is also incorrect because √32.4 equals approximately 5.7, which is another example of a non-terminating, non-repeating decimal. It cannot be accurately expressed as a simple fraction, thus categorizing it as an irrational number.
Conclusion
In summary, √2.56 is the only option that qualifies as a rational number because it can be expressed as a terminating decimal or a fraction. The other options are either irrational or cannot be expressed as a simple fraction, confirming that they do not meet the criteria for rational numbers.