Identify the following as rational or irrational numbers. Give the decimal representation of rational numbers:$ -\sqrt{64} $

Given:

\( -\sqrt{64} \)

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,

$-\sqrt{64}=-\sqrt{8\times8}$

$=-\sqrt{8^2}$

$=-8$

The decimal expansion of \( -\sqrt{64} \) is $-8$ and it is terminating.

Therefore, \( -\sqrt{64} \) is a rational number.      

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Updated on: 10-Oct-2022

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