Question

A rational number between $\sqrt{2}$ and $\sqrt{3}$ is

• A. $\frac{\sqrt{2}+\sqrt{3}}{2}$
• B. $\frac{\sqrt{2}\times \sqrt{3}}{2}$
• C. $1.5$
• D. $1.8$

Answer 1

The correct option is C

$1.5$

Explanation for the correct options:

Option(C): $\mathbf{1}\mathbf{.}\mathbf{5}$

We know that

$$\begin{gathered} \surd 2=1.4142135\dots . \\ \surd 3=1.732050807\dots \end{gathered}$$.

And, $1.41421....<1.5<1.73205....$

Hence, $1.5$ is lie between $\sqrt{2}$ and $\sqrt{3}$

And also$1.5$ is a terminating decimal which means it is a rational number.

Hence, this option is correct.

Explanation for Incorrect options:

Option(A): $\frac{\sqrt{\mathbf{2}}\mathbf{+}\sqrt{\mathbf{3}}}{\mathbf{2}}$

$\frac{(\surd 2+\surd 3)}{2}=1.57313218497\dots$ is a non-terminating and non-recurring decimal and therefore is an irrational number.

Hence, this option is incorrect.

Option(B): $\frac{\sqrt{\mathbf{2}}\mathbf{\times }\sqrt{\mathbf{3}}}{\mathbf{2}}$

$\frac{(\surd 2.\surd 3)}{2}=1.22474487139\dots$ is a non-terminating and non-recurring decimal and therefore is an irrational number.

Hence, this option is incorrect.

Option(D): $\mathbf{1}\mathbf{.}\mathbf{8}$

$1.8$ is a terminating decimal and is a rational number. But it is greater than $\sqrt{2}$ and $\sqrt{3}$

Thus, it does not lie between them.

Hence, this option is incorrect.

Hence, the correct option is (C)