Which of the following is a rational number? Square root of 23 Square root of 22 Square root of 24 Square root of 25
The Correct Answer and Explanation is:
Correct Answer: Square root of 25
A rational number is any number that can be expressed as a ratio of two integers, written in the form a/b, where a and b are integers and b ≠ 0. Rational numbers include integers, fractions, and terminating or repeating decimals.
Among the options given:
- √23
- √22
- √24
- √25
Only √25 is a rational number. This is because 25 is a perfect square, and its square root is 5, which is a whole number. A whole number can be written as 5/1, fitting the definition of a rational number.
In contrast, √23, √22, and √24 are not perfect squares. Their square roots result in non-terminating, non-repeating decimals, meaning they cannot be expressed exactly as a fraction of two integers. For example, the square root of 23 is approximately 4.7958…, but this decimal neither terminates nor repeats in a predictable pattern. This behavior classifies √23, √22, and √24 as irrational numbers.
A key property of square roots is that the square root of any non-perfect square positive integer always yields an irrational result. Perfect squares such as 1, 4, 9, 16, 25, 36, etc., when square-rooted, give integers, which are rational.
Hence, among the options provided, √25 is the only rational number. The rest represent irrational quantities because they cannot be neatly expressed as fractions or integers. This classification forms an important part of understanding the real number system, which includes both rational and irrational numbers.
