Question

11．計(jì)算：${（{\frac{1}{2}}）^{-2}}$sin45°+（$\sqrt{13}$+$\sqrt{5}$）⁰$-\;|{\;-\sqrt{18}\;}|$-$\frac{1}{{\sqrt{2}-1}}$-|$\sqrt{2}-3$|

Answer 1

分析 根據(jù)零指數(shù)冪、負(fù)整數(shù)指數(shù)冪和特殊角的三角函數(shù)值得到原式=4×$\frac{\sqrt{2}}{2}$+1-3$\sqrt{2}$-（$\sqrt{2}$-1）+$\sqrt{2}$-3，然后合并即可．

解答 解：原式=4×$\frac{\sqrt{2}}{2}$+1-3$\sqrt{2}$-（$\sqrt{2}$-1）+$\sqrt{2}$-3
=2$\sqrt{2}$+1-3$\sqrt{2}$-$\sqrt{2}$+1+$\sqrt{2}$-3
=-$\sqrt{2}$-1．

點(diǎn)評(píng) 本題考查了二次根式的計(jì)算：先把各二次根式化為最簡(jiǎn)二次根式，再進(jìn)行二次根式的乘除運(yùn)算，然后合并同類(lèi)二次根式．也考查了零指數(shù)冪、負(fù)整數(shù)指數(shù)冪和特殊角的三角函數(shù)值．