Simplify the following expressions:
(i) $(\sqrt{3}+\sqrt{7})^{2}$
(ii) $(\sqrt{5}-\sqrt{3})^{2}$
(iii) $(2 \sqrt{5}+3 \sqrt{2})^{2}$
(i) $(\sqrt{3}+\sqrt{7})^{2}$
As we know, $(a+b)^{2}=\left(a^{2}+2 \times a \times b+b^{2}\right)$
$=\sqrt{3^{2}}+2 \times \sqrt{3} \times \sqrt{7}+\sqrt{7^{2}}$
$=3+2 \times \sqrt{3 \times 7}+7$
$=10+2 \times \sqrt{21}$
(ii) $(\sqrt{5}-\sqrt{3})^{2}$
As we know, $(a-b)^{2}=\left(a^{2}-2 \times a \times b+b^{2}\right)$
$=(\sqrt{5})^{2}-2 \times \sqrt{5 \times 3}+(\sqrt{3})^{2}$
$=5-2 \sqrt{15}+3$
$=2-2 \sqrt{15}$
(iii) $(2 \sqrt{5}+3 \sqrt{2})^{2}$
As we know, $(a+b)^{2}=\left(a^{2}+2 \times a \times b+b^{2}\right)$
$=4 \sqrt{5 \times 5}+2 \times 2 \sqrt{5} \times 3 \sqrt{2}+9 \sqrt{2 \times 2}$
$=20+12 \sqrt{10}+18$
$=28+12 \sqrt{10}$