Question

Simplify the following expressions :

(i) $(4+\sqrt{7})(3+\sqrt{2})$

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

(iii) $(\sqrt{5}-2)(\sqrt{3}-\sqrt{5})$

Answer 1

(i) $(4+\sqrt{7})(3+\sqrt{2})$

$=4\times 3+4\sqrt{2}+3\sqrt{7}+\sqrt{7}\times \sqrt{2}$

$=12+4\sqrt{2}+3\sqrt{7}+\sqrt{14}$

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

$=3\times 5-3\sqrt{2}+5\sqrt{3}-\sqrt{3}\times \sqrt{2}$

$=15-3\sqrt{2}+5\sqrt{3}-\sqrt{6}$

(iii) $(\sqrt{5}-2)(\sqrt{3}-\sqrt{5})$

$=\sqrt{5}\times \sqrt{3}-\sqrt{5}\times \sqrt{5}-2\sqrt{3}+2\sqrt{5}$

$=\sqrt{15}-\sqrt{25}-2\sqrt{3}+2\sqrt{5}$

$=\sqrt{15}-5-2\sqrt{3}+2\sqrt{5}$

$=\sqrt{15}-2\sqrt{3}+2\sqrt{5}-5$