Examine whether the following numbers are rational or irrational:$ \sqrt{3}+\sqrt{5} $

Given:

\( \sqrt{3}+\sqrt{5} \)

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,

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

$\sqrt{5}=2.23606............$

The decimal expansion of \( \sqrt{3} \) and \( \sqrt{5} \) is non-terminating and non-recurring.

The sum of two irrational numbers is an irrational number.

Therefore, \( \sqrt{3}+\sqrt{5} \) is an irrational number.