Вычислить: [tex] \sqrt{10-2 \sqrt{21} } [/tex]. Created by Lidakim. algebra-ru

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August 2021 1 11 Report

Вычислить: [tex] \sqrt{10-2 \sqrt{21} } [/tex]

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NNNLLL54

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$\sqrt{10-2\sqrt21}=\sqrt{10-2\sqrt3\cdot \sqrt7}=\\\\=\sqrt{(\sqrt3)^2-2\sqrt3\cdot \sqrt7+(\sqrt7)^2}\\\\=\sqrt{(\sqrt3-\sqrt7)^2}=|\sqrt3-\sqrt7|=\sqrt7-\sqrt3$

Так как $\sqrt3-\sqrt7$ то

$|\sqrt3-\sqrt7|=-(\sqrt3-\sqrt7)=\sqrt7-\sqrt3$

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