Examine whether the following numbers are rational or irrational:$ 2+\sqrt{3} $

Given:

\( 2+\sqrt{3} \)

To do:

We have to classify the given number as rational or irrational.

Solution:  

A rational number can be expressed in either terminating decimal or non-terminating recurring decimals and an irrational number is expressed in non-terminating non-recurring decimals.

Therefore,

$\sqrt{3}=1.7320508..........$

The decimal expansion of \( \sqrt{3} \) is non-terminating and non-recurring.

The sum of a rational number and an irrational number is an irrational number.

Therefore, \( 2+\sqrt{3} \) is an irrational number.