Classify the rational and irrational numbers from the following :

(i) 5

(ii) $\dfrac{9}{14}$

(iii) $\sqrt{3}$

(iv) π

(v) 3.1416

(vi) $\sqrt{4}$

(vii) $-\sqrt{5}$

(viii) $\sqrt[3]{8}$

(ix) $\sqrt[3]{3}$

(x) $2\sqrt{6}$

(xi) $0.\overline{36}$

(xii) 0.202202220…

(xiii) $\dfrac{2}{\sqrt{3}}$

(xiv) $\dfrac{22}{7}$

Separate the rationals and irrationals from among the following numbers :

(i) -8

(ii) $\sqrt{25}$

(iii) $\dfrac{-3}{5}$

(iv) $\sqrt{8}$

(v) 0

(vi) π

(vii) $\sqrt[3]{5}$

(viii) $2.\overline{4}$

(ix) $-\sqrt{3}$

Write down the values of :

(i) $(2\sqrt{3})^2$

(ii) $\Big(\dfrac{3}{2}\sqrt{2}\Big)^2$

(iii) $(5 + \sqrt{3})^2$

(iv) $(\sqrt{6} - 3)^2$

(v) $(3 + 2\sqrt{5})^2$

(vi) $(\sqrt{5} + \sqrt{6})^2$

(vii) $\Big(\dfrac{3}{2\sqrt{2}}\Big)^2$

(viii) $(5 - 6\sqrt{3})^2$

State, giving reason, wether the given number is rational or irrational:

(i) $(3 + \sqrt{5})$

(ii) $(-1 + \sqrt{3})$

(iii) $5\sqrt{6}$

(iv) $-\sqrt{7}$

(v) $\dfrac{\sqrt{6}}{4}$

(vi) $\dfrac{3}{\sqrt{2}}$

(vii) $(3 + \sqrt{3}) (3 - \sqrt{3})$