[tex] \sqrt{9-4 \sqrt{5} }- \sqrt{5} [/tex] найти значение выражения. Created by vischneowa. algebra-ru

tex] найти значение выражения...

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[tex] \sqrt{9-4 \sqrt{5} }- \sqrt{5} [/tex] найти значение выражения

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red321

Verified answer

$\sqrt{9-4\sqrt{5}}=\sqrt{5-4\sqrt{5}+4}=\sqrt{(\sqrt{5})^2-2*2*\sqrt{5}+2^2}=\\=\sqrt{(\sqrt{5}-2})^2}=|\sqrt{5}-2}|=\sqrt{5}-2\\\\\sqrt{5}-2-\sqrt{5}=-2$

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