Question

Không dùng máy tính bỏ túi, hãy rút gọn biểu thức:

A = \(\left(\sqrt{26}+5\sqrt{2}\right)\sqrt{19-5\sqrt{13}}\)

Answer 1

A=(\(\sqrt{13}\).\(\sqrt{2}\)+5\(\sqrt{2}\))\(\sqrt{19-5\sqrt{13}}\)

   =(\(\sqrt{13}\)+5)\(\sqrt{2}\). \(\sqrt{19-5\sqrt{13}}\)

   =(\(\sqrt{13}\)+5) \(\sqrt{2\left(19-5\sqrt{13}\right)}\)

   = (\(\sqrt{13}\)+5) \(\sqrt{38-2.5\sqrt{13}}\)

   =(\(\sqrt{13}\)+5) \(\sqrt{5^2-2.5\sqrt{13}+13}\)

   =(\(\sqrt{13}\)+5)\(\sqrt{\left(5-\sqrt{13}\right)^2}\)

   =(\(\sqrt{13}\)+5) \(|5-\sqrt{13}|\)

   =(5+\(\sqrt{13}\))(5-\(\sqrt{13}\))

   = 25-13 = 12