Question

8．計(jì)算：（-3）⁰-$\root{3}{27}$+|1-$\sqrt{2}$|+$\sqrt{2}$×$\sqrt{6}$+（$\sqrt{3}$+$\sqrt{2}$）^-1．

Answer 1

分析 直接利用負(fù)整數(shù)指數(shù)冪的性質(zhì)以及零指數(shù)冪的性質(zhì)和絕對(duì)值的性質(zhì)分別化簡求出答案．

解答 解：（-3）⁰-$\root{3}{27}$+|1-$\sqrt{2}$|+$\sqrt{2}$×$\sqrt{6}$+（$\sqrt{3}$+$\sqrt{2}$）^-1
=1-3+$\sqrt{2}$-1+2$\sqrt{3}$+$\sqrt{3}$-$\sqrt{2}$
=3$\sqrt{3}$-3．

點(diǎn)評(píng) 此題主要考查了負(fù)整數(shù)指數(shù)冪的性質(zhì)以及零指數(shù)冪的性質(zhì)和絕對(duì)值的性質(zhì)，正確化簡各數(shù)是解題關(guān)鍵．