Examine whether the following numbers are rational or irrational:$ \sqrt{23} $

Given:

\( \sqrt{23} \)

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,

$\sqrt{23}=4.7958315............$

The decimal expansion of \( \sqrt{23} \) is non-terminating and non-recurring.

Therefore, \( \sqrt{23} \) is an irrational number.   

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Updated on: 10-Oct-2022

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