Question

3．计算：-3²+6cos45°-$\sqrt{2}$（2-$\sqrt{2}$）+|$\sqrt{2}$-3|．

Answer 1

分析 首先利用特殊角的三角函数结合绝对值的性质分别化简，进而求出答案．

解答 解：-3²+6cos45°-$\sqrt{2}$（2-$\sqrt{2}$）+|$\sqrt{2}$-3|
=-9+6×$\frac{\sqrt{2}}{2}$-2$\sqrt{2}$-2+3-$\sqrt{2}$
=-9+3$\sqrt{2}$-2$\sqrt{2}$+1-$\sqrt{2}$
=-8．

点评 此题主要考查了二次根式的混合运算，正确化简各数是解题关键．