Question

15．計(jì)算：|$\sqrt{3}-\sqrt{2}$|+（$\sqrt{2015}-1$）⁰+2sin45°-2cos30°+（$\frac{1}{2015}$）^-1．

Answer 1

分析 直接利用零指數(shù)冪的性質(zhì)以及絕對(duì)值的性質(zhì)、負(fù)整數(shù)指數(shù)冪的性質(zhì)、特殊角的三角函數(shù)值分別化簡(jiǎn)求出答案．

解答 解：|$\sqrt{3}-\sqrt{2}$|+（$\sqrt{2015}-1$）⁰+2sin45°-2cos30°+（$\frac{1}{2015}$）^-1
=$\sqrt{3}$-$\sqrt{2}$+1+2×$\frac{\sqrt{2}}{2}$-2×$\frac{\sqrt{3}}{2}$+2015
=$\sqrt{3}$-$\sqrt{2}$+1+$\sqrt{2}$-$\sqrt{3}$+2015
=2016．

點(diǎn)評(píng) 此題主要考查了實(shí)數(shù)運(yùn)算，根據(jù)相關(guān)運(yùn)算法則正確化簡(jiǎn)是解題關(guān)鍵．