Show that x is irrational, if :

(i) x² = 6

(ii) x² = 0.009

(iii) x² = 27

(i) Given,

⇒ x² = 6

⇒ x = $\sqrt{6}$

⇒ x = 2.449…..

Since, x is non-terminating as well as non-recurring.

Hence, proved that x is irrational.

(ii) Given,

⇒ x² = 0.009

⇒ x = $\sqrt{0.009}$

⇒ x = 0.094…..

Since, x is non-terminating as well as non-recurring.

Hence, proved that x is irrational.

(iii) Given,

⇒ x² = 27

⇒ x = $\sqrt{27}$

⇒ x = 5.196…..

Since, x is non-terminating as well as non-recurring.

Hence, proved that x is irrational.