Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:$ 3 \sqrt{18} $

Given:

\( 3\sqrt{18} \)

To do:

We have to identify the given number as rational or irrational and write its decimal representation.

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,

$3\sqrt{18}=3\sqrt{9\times2}$

$=3\sqrt{3^2\times2}$

$=3\times3\sqrt{2}$

$=9\sqrt{2}$

$\sqrt{2}=1.4142135623..........$

$\Rightarrow 9\sqrt{2}=9\times1.4142135623...........$

$=12.727922061..........$

The decimal expansion of \( 3\sqrt{18} \) is $12.727922061..........$ and it is non-terminating non-recurring.

Therefore, \( 3\sqrt{18} \) is an irrational number.   

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Updated on: 10-Oct-2022

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