Which of the following is a rational number? 

Concept -

Rational Number - 

A rational number is any number that can be expressed as the quotient or fraction \(\frac{p}{q}\), where p and  q  are integers and q is not equal to zero.

In other words, a rational number is a number that can be written in the form of a fraction where both the numerator and denominator are integers.

Rational numbers include integers (since they can be expressed as a fraction with a denominator of 1) and fractions such as \(\frac{3}{4}\) , \(\frac{5}{6}\) ,  \(\frac{7}{1} \), etc. They can be positive, negative, or zero and can be represented as terminating decimals or repeating decimals.

For example, 0.5  is a rational number because it can be written as \( \frac{1}{2}\)  in fraction form, and 1.333...  (repeating decimal for  \(\frac{4}{3}\) is also a rational number.

Irrational Number -

An irrational number is a real number that cannot be expressed as a simple fraction (i.e., a ratio of two integers). These numbers have non-repeating, non-terminating decimal representations. They cannot be written as a quotient of two integers and have an infinite number of decimal places without exhibiting any repeating pattern. Examples include the square root of non-perfect squares (like √2 or √3), transcendental numbers (like π or e), and various mathematical constants.

Explanation -

(1) 2 - √3  is an irrational number as √3  is an irrational number.  

(2) √5 is an irrational number

(3) \(\frac{2\sqrt3}{\sqrt3}\) = 2 is a rational number

(4) √6  is an irrational number.

Hence the correct answer is \(\frac{2\sqrt3}{\sqrt3}\).