Simplify the following expressions:

Solution:

(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, $(a+b)^{2}=\left(a^{2}+2 \times a \times b+b^{2}\right)$

$=4 \sqrt{5 \times 5}+2 \times 2 \sqrt{5} \times 3 \sqrt{2}+9 \sqrt{2 \times 2}$

$=20+12 \sqrt{10}+18$

$=28+12 \sqrt{10}$