Simplify the following expressions:

Question:

Simplify the following expressions:

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

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

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

 

Solution:

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

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

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

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

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

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

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

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

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

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

 

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