Question

12．若对实数a，b，c，d规定运算$|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|$=ad-bc，则$|\begin{array}{l}{1}&{\sqrt{2}}\\{-3}&{\sqrt{8}}\end{array}|$=5$\sqrt{2}$．

Answer 1

分析 根据题意将原式变形，进而利用二次根式的性质化简合并即可．

解答 解：∵$|\begin{array}{l}{a}&{b}\\{c}&{d}\end{array}|$=ad-bc，
∴$|\begin{array}{l}{1}&{\sqrt{2}}\\{-3}&{\sqrt{8}}\end{array}|$=$\sqrt{8}$+3$\sqrt{2}$=2$\sqrt{2}$+3$\sqrt{2}$=5$\sqrt{2}$．
故答案为：$5\sqrt{2}$．

点评 此题主要考查了二次根式的加减运算，正确掌握运算法则是解题关键．