 # Find which of the variables x, y, z `
Question:

Find which of the variables $x, y, z$ and $u$ represent rational numbers and which irrational numbers.

(i) $x^{2}=5$

(ii) $y^{2}=9$

(iii) $z^{2}=0.04$

(iv) $u^{2}=17 / 4$

Solution:

(i) Given,                          $x^{2}=5$

On taking square root both sides we get

$x=\pm \sqrt{5}$             [irrational number]

(ii) Given,                         $y^{2}=9$

On taking square root both sides, we get

$y=\pm \sqrt{9}=\pm 3$            [rational number]

(iii) Given,                        $z^{2}=0.04$

On taking square root both sides, we get

$z=\sqrt{0.04}=\sqrt{\frac{4}{100}}=\frac{2}{10}$ [rational number]                        $\left[\because \frac{p}{q}\right.$ form, $q \neq 0, p$ and $q$ are integers $]$

(iv) Given,                              $u^{2}=\frac{17}{4}$

On taking square root both sides, we get

$u=\pm \sqrt{\frac{17}{4}}=\pm \frac{\sqrt{17}}{2}$                [irrational number because numerator is irrational]