If x = $\sqrt{3} - \sqrt{2}$, find the value of :

(i) $x + \dfrac{1}{x}$

(ii) $x^2 + \dfrac{1}{x^2}$

(iii) $x^3 + \dfrac{1}{x^3}$

(iv) $x^3 + \dfrac{1}{x^3} - 3\Big(x^2 + \dfrac{1}{x^2}\Big) + x + \dfrac{1}{x}$

State true or false :

(i) Negative of an irrational number is irrational.

(ii) The product of a non-zero rational number and an irrational number is a rational number.

Draw a line segment of length $\sqrt{8}$ cm.

Show that :

$x^3 + \dfrac{1}{x^3} = 52$, if x = 2 + $\sqrt{3}$