Question

Tính A= sqrt(20 + 14sqrt(2)) + sqrt(20 - 14sqrt(2))

Answer 1

\(A=\sqrt{20+14\sqrt{2}}+\sqrt{20-14\sqrt{2}}>0\)

\(\Rightarrow A^2=\left(\sqrt{20+14\sqrt{2}}+\sqrt{20-14\sqrt{2}}\right)^2\)

\(=20+14\sqrt{2}+2\sqrt{\left(20+14\sqrt{2}\right)\left(20-14\sqrt{2}\right)}+20-14\sqrt{2}\)

\(=40+2\sqrt{20^2-14^2.2}\)

\(=40+2\sqrt{8}\)

\(=40+4\sqrt{2}\)

\(\Rightarrow A=\sqrt{40+4\sqrt{2}}\) (do A dương).

\(=2\sqrt{10+\sqrt{2}}\)