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電子課本網 第109頁

第109頁

信息發(fā)布者:
?$解:矩形的另外一條邊長為?2\sqrt {6}÷\sqrt {2}=2\sqrt {3}\mathrm {cm}?$?
?$ 對角線的長為?\sqrt {(\sqrt {2})2+(2\sqrt {3})2}=\sqrt {14}\mathrm {cm}?$?
?$ \sqrt{3}$?
?$ \frac{\sqrt{5}}{5}$?
?$解:(2)①原式=\frac {2(\sqrt{5}-\sqrt{3})}{(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}$?
?$=\sqrt{5}-\sqrt{3}$?
?$②原式=\frac {5-3}{\sqrt{5}+\sqrt{3}}$?
?$=\frac {(\sqrt{5})2-(\sqrt{3})2}{\sqrt{5}+\sqrt{3}}$?
?$=\frac {(\sqrt{5}+\sqrt{3})(\sqrt{5}-\sqrt{3})}{\sqrt{5}+\sqrt{3}}$?
?$=\sqrt{5}-\sqrt{3}$?
?$(3)原式=\frac{1}{2}(\sqrt{3}-1+\sqrt{5}-\sqrt{3}+\sqrt{7}-\sqrt{5}+...+\sqrt{2n+1}-\sqrt{2n-1})$?
?$=\frac{1}{2}(\sqrt{2n+1}-1)$?
?$? \frac {\sqrt {3}}{3}?$?
?$\sqrt{6}$?
?$? \frac {\sqrt {2}}{2}?$?
?$ \frac{\sqrt{6}}{2}$?
?$\frac{\sqrt{6}}{3}$?
?$\frac{\sqrt{6}}{6}$?