Question

5．简便计算：$\frac{8-\sqrt{2}}{\sqrt{2}}•\frac{\sqrt{3}}{3\sqrt{3}+\sqrt{6}}•\frac{7}{13\sqrt{2}-11}$．

Answer 1

分析 首先将前两项化简，进而将前两项相乘，再和后面式子相乘得出即可．

解答 解：$\frac{8-\sqrt{2}}{\sqrt{2}}•\frac{\sqrt{3}}{3\sqrt{3}+\sqrt{6}}•\frac{7}{13\sqrt{2}-11}$
=（4$\sqrt{2}$-1）×$\frac{1}{3+\sqrt{2}}$×$\frac{7}{13\sqrt{2}-11}$
=（4$\sqrt{2}$-1）×$\frac{3-\sqrt{2}}{7}$×$\frac{7}{13\sqrt{2}-11}$
=（4$\sqrt{2}$-1）（3-$\sqrt{2}$）×$\frac{1}{13\sqrt{2}-11}$
=（12$\sqrt{2}$-8-3+$\sqrt{2}$）×$\frac{1}{13\sqrt{2}-11}$
=（13$\sqrt{2}$-11）×$\frac{1}{13\sqrt{2}-11}$
=1．

点评 此题主要考查了二次根式的混合运算，正确化简二次根式是解题关键．