Question

5．計(jì)算：$\sqrt{27}$×$\sqrt{6}$-|1-$\sqrt{2}$|+$\sqrt{2}$cos45°．

Answer 1

分析 根據(jù)特殊角的三角函數(shù)值和絕對值的意義得到原式=3$\sqrt{3}$×$\sqrt{6}$+（1-$\sqrt{2}$）+$\sqrt{2}$×$\frac{\sqrt{2}}{2}$，然后進(jìn)行二次根式的乘法運(yùn)算后合并即可．

解答 解：原式=3$\sqrt{3}$×$\sqrt{6}$+（1-$\sqrt{2}$）+$\sqrt{2}$×$\frac{\sqrt{2}}{2}$
=9$\sqrt{2}$+1-$\sqrt{2}$+1
=8$\sqrt{2}$+2．

點(diǎn)評 本題考查了二次根式的計(jì)算：先把各二次根式化為最簡二次根式，再進(jìn)行二次根式的乘除運(yùn)算，然后合并同類二次根式．