In the following equations, find whether variables $w$ represent rational or irrational numbers
$w^{2} = 27$

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Solution

$w^{2} = 27$
$\Rightarrow w = \sqrt{27}$
The number $\sqrt{27}$ is an irrational number.
Hence, $w$ represents an irrational number.

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In the following equations, find which variables x, y, z etc, represent rational or irrational numbers :

(i) $x^{2}$ = 5 (ii) $y^{2}$ = 9

(iii) $z^{2}$ = 0.04 (iv) $u^{2} = \frac{17}{4}$

(v) $v^{2}$ = 3 (vi) $w^{2}$ = 27

(vii) $t^{2} = 0.4$

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