Question

Write any one rational number between \[\sqrt{2}\] and \[\sqrt{3}\].

Answer 1

Hint: At first convert the irrational numbers \[\sqrt{2}\], \[\sqrt{3}\] into approximate rational decimal expansions and then write any rational number more than approximations of \[\sqrt{2}\] but less than that of \[\sqrt{3}\].

Complete step-by-step answer:
In the question we are said to write one rational number between \[\sqrt{2}\] and \[\sqrt{3}\].
Before proceeding let’s briefly describe rational numbers.
The rational numbers are numbers which can be expressed as a fraction and also as positive integers, negative integers and 0. It can be written as \[\dfrac{p}{q}\] form where q is not equal to ‘0’.
Rational word is derived from the word ratio which actually means comparison between two or more values or more values or integers numbers and is known as fractions. In simple word, it is ratio of integers.
Example: \[\dfrac{3}{2}\] is a rational number.
Now we will write the decimal representations of both square root to as many digits as we can or want to write.
So, we can write \[\sqrt{2}\], \[\sqrt{3}\] as:
\[\begin{align}
  & \sqrt{2}\approx 1.4142136.... \\
 & \sqrt{3}\approx 1.7320508..... \\
\end{align}\]
Here ‘\[\approx \]’ sign means approximation.
So any decimal number which can be written in fraction form can be taken as answer of it lies between decimal approximations of \[\sqrt{2}\] and \[\sqrt{3}\].
So, the rational number is 1.5.
Hence the answer is \[\dfrac{15}{10}\].

Note: Students should know the definition and basics of rational numbers. Also between two irrational numbers there are infinite rational numbers and between 2 rational numbers there are infinite irrational numbers.