In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:$ z^{2}=0.04 $

Given:

\( z^{2}=0.04 \)

To do:

We have to find whether $z$ represents a rational number or an irrational number.

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.

$z^2=0.04$

$\Rightarrow z^2=(\pm \sqrt{0.2})^2$

$\Rightarrow z=\pm 0.2$

$0.2$ is a rational number.

Therefore, \( z \) is a rational number.       

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Updated on: 10-Oct-2022

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