Question

19．計(jì)算：$\sqrt{18}$+$\sqrt{\frac{9}{2}}$-${（π-\sqrt{2}）}^{0}$-|1-$\sqrt{2}$|+${（\frac{1}{2}）}^{-1}$．

Answer 1

分析 本題涉及零指數(shù)冪、絕對(duì)值、負(fù)整數(shù)指數(shù)冪、二次根式化簡(jiǎn)四個(gè)考點(diǎn)．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 原式=3$\sqrt{2}$+$\frac{3\sqrt{2}}{2}$-1-$\sqrt{2}$+1+2
=$\frac{7}{2}\sqrt{2}$+2．

點(diǎn)評(píng) 本題考查實(shí)數(shù)的綜合運(yùn)算能力，熟練掌握負(fù)整數(shù)指數(shù)冪、零指數(shù)冪、二次根式、絕對(duì)值等考點(diǎn)的運(yùn)算是解題的關(guān)鍵．