In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:$ t^{2}=0.4 $

Given:

\( t^{2}=0.4 \)

To do:

We have to find whether $t$ 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.

$t^2=0.4$

$\Rightarrow t^2=(\sqrt{0.4})^2$

$\Rightarrow t=\sqrt{0.4}$

$\Rightarrow t=2\sqrt{0.1}$

$\Rightarrow t=2\sqrt{\frac{1}{10}}$

$\Rightarrow t=\frac{2}{\sqrt{10}}$

$\sqrt{10}$ is an irrational number.

Therefore, \( t \) is an irrational number.           

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Updated on: 10-Oct-2022

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