Question

tách :

\(\sqrt{17+12\sqrt{2}}\)

 

Answer 1

\(\sqrt{17+12\sqrt{2}}=\sqrt{3+12\sqrt{2}+\left(2\sqrt{2}\right)^2}=\sqrt{\left(3+2\sqrt{2}\right)^2}=3+2\sqrt{2}\)

Answer 2

\(\sqrt{17+12\sqrt{2}}=\sqrt{17+2\sqrt{72}}=\sqrt{9+2\sqrt{8}.\sqrt{9}+8}=\sqrt{\left(3+\sqrt{8}\right)^2}=3+\sqrt{8}\)