Question

Question 1
Find which of the variables x,y,z and u represent rational numbers and which irrational numbers:
$\left(i\right)x^2=5\left(ii\right)y^2=9\left(iii\right)z^2=0.04\left(iv\right)u^2=\frac{17}{4}$

Answer 1

(i) Given
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]
$[\because \frac{p}{q}form,q\ne 0pandqareintegers]$
(iv) Given $u^2=\frac{17}{4}$
On taking square root both , we get
$u=\pm \sqrt{\frac{17}{4}}=\pm \frac{\sqrt{17}}{2}$
[ irrational number because numerator is irrational]