Question

8．計(jì)算：|1-$\sqrt{2}$|-$\sqrt{8}$+（-1）²⁰¹⁶+（$\frac{1}{2}$）^-3．

Answer 1

分析 此題涉及絕對(duì)值、負(fù)整數(shù)指數(shù)冪、有理數(shù)的乘方、算術(shù)平方根，在計(jì)算時(shí)，需要針對(duì)每個(gè)考點(diǎn)分別進(jìn)行計(jì)算，然后根據(jù)實(shí)數(shù)的運(yùn)算法則求得計(jì)算結(jié)果．

解答 解：|1-$\sqrt{2}$|-$\sqrt{8}$+（-1）²⁰¹⁶+（$\frac{1}{2}$）^-3
=$\sqrt{2}$-1-2$\sqrt{2}$+1+8
=8-$\sqrt{2}$

點(diǎn)評(píng) 此題主要考查了實(shí)數(shù)的綜合運(yùn)算能力，解決此類題目的關(guān)鍵是熟練掌握負(fù)整數(shù)指數(shù)冪、有理數(shù)的乘方、算術(shù)平方根、絕對(duì)值等的運(yùn)算．