Question

Simplify: (- √5- √7)(√2- 3)

Answer 1

$( - \sqrt{5} - \sqrt{7})(\sqrt{2} - 3 ) \\= - ( \sqrt{5} + \sqrt{7})(\sqrt{2} - 3 )\\= - [ \sqrt{5}(\sqrt{2} - 3) + \sqrt{7}( \sqrt{2} - 3 )] \\= - [ \sqrt{5} \times \sqrt{2} - \sqrt{5} \times 3 + \sqrt{7} \times \sqrt{2} - \sqrt{7} \times 3 ] \\=- ( \sqrt{10} -3\sqrt{5} + \sqrt{14} - 3\sqrt{7} ) \\= - \sqrt{10} +3\sqrt{5} - \sqrt{14} + 3\sqrt{7}$

Therefore.,

$\red{ ( - \sqrt{5} - \sqrt{7})(\sqrt{2} - 3 )} \\\green {= - \sqrt{10} +3\sqrt{5} - \sqrt{14} + 3\sqrt{7} }$

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