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

(i) Solving,

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

$\Rightarrow 2\sqrt{3} \times 2\sqrt{3}$

⇒ 4 × 3

⇒ 12.

Hence, $(2\sqrt{3})^2$ = 12.

(ii) Solving,

$\Rightarrow \Big(\dfrac{3}{2}\sqrt{2}\Big)^2 \\[1em] \Rightarrow \dfrac{3}{2}\sqrt{2} \times \dfrac{3}{2}\sqrt{2} \\[1em] \Rightarrow \dfrac{9}{4} \times 2 \\[1em] \Rightarrow \dfrac{9}{2}.$

Hence, $\Big(\dfrac{3}{2}\sqrt{2}\Big)^2 = \dfrac{9}{2}$.

(iii) Solving,

$\Rightarrow (5 + \sqrt{3})^2 \\[1em] \Rightarrow (5)^2 + (\sqrt{3})^2 + 2 \times 5 \times \sqrt{3} \\[1em] \Rightarrow 25 + 3 + 10\sqrt{3} \\[1em] \Rightarrow 28 + 10\sqrt{3}$

Hence, $(5 + \sqrt{3})^2 = 28 + 10\sqrt{3}$.

(iv) Solving,

$\Rightarrow (\sqrt{6} - 3)^2 \\[1em] \Rightarrow (\sqrt{6})^2 + (3)^2 - 2 \times 3 \times \sqrt{6} \\[1em] \Rightarrow 6 + 9 - 6\sqrt{6} \\[1em] \Rightarrow 15 - 6\sqrt{6}$

Hence, $(\sqrt{6} - 3)^2 = 15 - 6\sqrt{6}$.

(v) Solving,

$\Rightarrow (3 + 2\sqrt{5})^2 \\[1em] \Rightarrow (3)^2 + (2\sqrt{5})^2 + 2 \times 3 \times 2\sqrt{5} \\[1em] \Rightarrow 9 + 4 \times 5 + 12\sqrt{5} \\[1em] \Rightarrow 9 + 20 + 12\sqrt{5} \\[1em] \Rightarrow 29 + 12\sqrt{5}$

Hence, $(3 + 2\sqrt{5})^2 = 29 + 12\sqrt{5}$.

(vi) Solving,

$\Rightarrow (\sqrt{5} + \sqrt{6})^2 \\[1em] \Rightarrow (\sqrt{5})^2 + (\sqrt{6})^2 + 2 \times \sqrt{5} \times \sqrt{6} \\[1em] \Rightarrow 5 + 6 + 2\sqrt{30} \\[1em] \Rightarrow 11 + 2\sqrt{30}$

Hence, $(\sqrt{5} + \sqrt{6})^2 = 11 + 2\sqrt{30}$.

(vii) Solving,

$\Rightarrow \Big(\dfrac{3}{2\sqrt{2}}\Big)^2 \\[1em] \Rightarrow \dfrac{3}{2\sqrt{2}} \times \dfrac{3}{2\sqrt{2}} \\[1em] \Rightarrow \dfrac{9}{4 \times 2} \\[1em] \Rightarrow \dfrac{9}{8}$

Hence, $\Big(\dfrac{3}{2\sqrt{2}}\Big)^2 = \dfrac{9}{8}$.

(viii) Solving,

$\Rightarrow (5 - 6\sqrt{3})^2 \\[1em] \Rightarrow (5)^2 + (6\sqrt{3})^2 - 2 \times 5 \times 6\sqrt{3} \\[1em] \Rightarrow 25 + 108 - 60\sqrt{3} \\[1em] \Rightarrow 133 - 60\sqrt{3}$

Hence, $(5 - 6\sqrt{3})^2 = 133 + 60\sqrt{3}$.