Question

Simplify the following expressions :

(i) $(\sqrt{3}+\sqrt{7}{)}^2$

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

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

Answer 1

(i) $(\sqrt{3}+\sqrt{7}{)}^2$

$=(\sqrt{3}{)}^2+(\sqrt{7}{)}^2+2\times \sqrt{3}\times \sqrt{7}\{\because (a+b{)}^2=a^2+b^2+2ab\}=3+7+2\sqrt{21}=10+2\sqrt{21}$

(ii) $(\sqrt{5}-\sqrt{3}{)}^2=(\sqrt{5}{)}^2+(\sqrt{3}{)}^2-2\times \sqrt{5}\times \sqrt{3}\{\because (a-b{)}^2=a^2+b^2-2ab\}=5+3-2\sqrt{15}=8-2\sqrt{15}$

(iii) $(2\sqrt{5}+3\sqrt{2}{)}^2=(2\sqrt{5}{)}^2+(3\sqrt{2}{)}^2+2\times 2\sqrt{5}\times 3\sqrt{2}\{\because (a+b{)}^2=a^2+b^2+2ab\}=4\times 5+9\times 2+2\times 2\times 3\times \sqrt{5}\times \sqrt{2}=20+18+12\sqrt{10}=38+12\sqrt{10}$