Show that x is rational, if :

(i) x² = 16

(ii) x² = 0.0004

(iii) x² = $1\dfrac{7}{9}$

(i) Given,

⇒ x² = 16

⇒ x = $\sqrt{16}$

⇒ x = $\pm 4$.

Integers are considered as rational numbers.

Hence, proved that x is rational.

(ii) Given,

⇒ x² = 0.0004

⇒ x = $\sqrt{0.0004}$

⇒ x = $0.02$.

Terminating decimals are considered as rational numbers.

Hence, proved that x is rational.

(iii) Given,

⇒ x² = $1\dfrac{7}{9}$

⇒ x² = $\dfrac{16}{9}$

⇒ x = $\sqrt{\dfrac{16}{9}}$

⇒ x = $\dfrac{4}{3}$ = 1.333…..

Recurring decimals are considered as rational number.

Hence, proved that x is rational.