Question

Rút gọn:  A= \(\sqrt{13+\sqrt{2}+5\sqrt{1+2\sqrt{2}}}+\sqrt{13+\sqrt{2}-5\sqrt{1+2\sqrt{2}}}\)

Answer 1

A>0

\(A^2=26+2\sqrt{2}+2\sqrt{\left(13+\sqrt{2}\right)^2-25\left(1+2\sqrt{2}\right)}\)

      \(=26+2\sqrt{2}+2\sqrt{171+26\sqrt{2}-25-50\sqrt{2}}\)  

    \(=26+2\sqrt{2}+2.\sqrt{144-2.12\sqrt{2}+2}\)

   \(=26+2\sqrt{2}+2.\left(12-\sqrt{2}\right)\)

  \(=50\)

\(A=\sqrt{50}=5\sqrt{2}\)

Answer 2

tham khảo câu hỏi tương tự nha bạn