Question

Write a rational number between $\sqrt{2}$ and $\sqrt{3}$.
( a ) $\dfrac{3}{2}$
( b ) $\dfrac{4}{2}$
( c )$\dfrac{5}{2}$
( d ) 5

Answer 1

Hint: Before solving this question we must know the value of square roots of 2 and 3 which will help us to solve the question very easily. Also, one must know what is a rational number as it will let us choose the appropriate options.

Complete step-by-step solution:
Now, before solving the question let us talk about numbers which are called rational numbers.
In the world of mathematics, the number which is called a rational number are those numbers that can be expressed as the quotient or fraction that is $\dfrac{p}{q}$ of two numbers where q cannot be equals to 0. Now, if q equals to 1, then it gives integer value. So, every integer is a rational number.
Now, in question, it is given that we have to find a number which is rational and also it lies between $\sqrt{2}$ and $\sqrt{3}$.
Now, first let see the options which are $\dfrac{3}{2}$, $\dfrac{4}{2}$, $\dfrac{5}{2}$ and 5 and all are rational numbers.
Now, what we will do is, we will find the values of $\dfrac{3}{2}$, $\dfrac{4}{2}$, $\dfrac{5}{2}$ and 5 in integral or decimal form
So, $\dfrac{3}{2}=1.5$ , $\dfrac{4}{2}=2$, $\dfrac{5}{2}=2.5$ and 5.
Now, we know that $\sqrt{2}$ approximately equals to 1.414, and $\sqrt{3}$ approximately equals 1.732.
Now, on seeing the values of $\sqrt{2}=1.414$ and $\sqrt{3}=1.732$ and comparing them with options which are 1.5 , 2 , 2.5 and 5 we see that only 1.5 is the number which is rational and lies between $\sqrt{2}$ and $\sqrt{3}$.
Hence, option ( a ) is correct.

Note: One must know the difference between rational and irrational number so that he can discard the options on the basis of definition and also one must know the values of $\sqrt{2}$ and $\sqrt{3}$ as it makes one solve the question easily and very fast.