Question

7．計(jì)算：（$\frac{1}{2}$）^-1+|1-$\sqrt{2}$|-$\sqrt{27}$tan30°．

Answer 1

分析 直接利用負(fù)整指數(shù)冪的性質(zhì)以及絕對(duì)值的性質(zhì)和特殊角的三角函數(shù)值分別化簡(jiǎn)求出答案．

解答 解：（$\frac{1}{2}$）^-1+|1-$\sqrt{2}$|-$\sqrt{27}$tan30°
=2+$\sqrt{2}$-1-3$\sqrt{3}$×$\frac{\sqrt{3}}{3}$
=1+$\sqrt{2}$-3
=$\sqrt{2}$-2．

點(diǎn)評(píng) 此題主要考查了負(fù)整指數(shù)冪的性質(zhì)以及絕對(duì)值的性質(zhì)和特殊角的三角函數(shù)值，正確化簡(jiǎn)各數(shù)是解題關(guān)鍵．