Question

Rezultatul calculului
$( \sqrt{3} + \sqrt{6} ) {}^{2} - ( \sqrt{2} - \sqrt{5} )^{2}$

Answer 1

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Answer 2

$( \sqrt{3} + \sqrt{6}) ^{2} - {( \sqrt{2} - \sqrt{5} })^{2} = \\ \\ { \sqrt{3} }^{2} + 2 \sqrt{3} \sqrt{6} + { \sqrt{6} }^{2} - { \sqrt{2} }^{2} + 2 \sqrt{2} \sqrt{5} - { \sqrt{5} }^{2} = \\ \\ 3 + 2 \sqrt{3} \sqrt{6} + 6 - 2 + 2 \sqrt{2} \sqrt{5} - 5 = \\ \\ 3 + 2 \sqrt{3 \times 6} + 6 - 2 + 2 \sqrt{2} \sqrt{5} - 5 = \\ \\ 3 + 2 \sqrt{18} + 6 - 2 + 2 \sqrt{2} \sqrt{5} - 5 = \\ \\ 3 + 2 \times 3 \sqrt{2} + 6 - 2 + 2 \sqrt{2} \sqrt{5} - 5 \\ \\ 3 + 6 \sqrt{2} + 6 - 2 + 2 \sqrt{2} \sqrt{5} - 5 = \\ \\ 3 + 6 \sqrt{2} + 6 - 2 + 2 \sqrt{2 \times 5} - 5 = \\ \\ 3 + 6 \sqrt{2} + 6 - 2 + 2 \sqrt{10} - 5 = \\ \\ (3 + 6 - 2 - 5) + 6 \sqrt{2} + 2 \sqrt{10} = 2 + 6 \sqrt{2} + 2 \sqrt{10}$