In the following equation, find which variables $x, y, z$ etc. represent rational or irrational numbers:$ w^{2}=27 $
Given:
\( w^{2}=27 \)
To do:
We have to find whether $w$ 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.
$w^2=27$
$\Rightarrow w^2=(\sqrt{27})^2$
$\Rightarrow w=\sqrt{9\times3}$
$\Rightarrow w=\sqrt{3^2\times3}$
$\Rightarrow w=3\sqrt{3}$
$\sqrt{3}$ is an irrational number.
$\Rightarrow w=3\sqrt{3}$ is an irrational number.
Therefore, \( w \) is an irrational number.
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