Question

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Answer 1

Ответ:

1

Объяснение:

$\sqrt{2+\sqrt3}}\sqrt{2+\sqrt{2+\sqrt3}}}\sqrt{2+\sqrt{2+\sqrt{2+\sqrt3}}}}\sqrt{2-\sqrt{2+\sqrt{2+\sqrt3}}}}=$

$=\sqrt{2+\sqrt3}}\sqrt{2+\sqrt{2+\sqrt3}}}\sqrt{{(2+\sqrt{2+\sqrt{2+\sqrt3}}})(2-\sqrt{2+\sqrt{2+\sqrt3}}})}=$

$=\sqrt{2+\sqrt3}\sqrt{2+\sqrt{2+\sqrt3}}\sqrt{4-(2+\sqrt{2+\sqrt3}})=$

$=\sqrt{2+\sqrt3}\sqrt{2+\sqrt{2+\sqrt3}}\sqrt{2-\sqrt{2+\sqrt3}}=$$=\sqrt{2+\sqrt3}\sqrt{(2+\sqrt{2+\sqrt3})(2-\sqrt{2+\sqrt3})}=$

$=\sqrt{2+\sqrt3}}\sqrt{4-(2+\sqrt3)}}=\sqrt{2+\sqrt3}}\sqrt{2-\sqrt3}=$

$=\sqrt{(2+\sqrt3)(2-\sqrt3)}=\sqrt{4-3}=\sqrt{1}=1$