Question

Rút gọn:  \(\sqrt{17-12\sqrt{2}}+\sqrt{17+12\sqrt{2}}\)

Answer 1

\(\sqrt{17-12\sqrt{2}}+\sqrt{17+12\sqrt{2}}=\sqrt{17-2\sqrt{72}}+\sqrt{17+2\sqrt{72}}\)

=\(\sqrt{9-2\sqrt{9}.\sqrt{8}+8}+\sqrt{9+2\sqrt{9}.\sqrt{8}+8}\)

=\(\sqrt{\left(\sqrt{9}-\sqrt{8}\right)^2}+\sqrt{\left(\sqrt{9}+\sqrt{8}\right)^2}\)

=\(\sqrt{9}-\sqrt{8}+\sqrt{9}+\sqrt{8}=3+3=6\)

Answer 2

\(\sqrt{17-12\sqrt{2}}+\sqrt{17+12\sqrt{2}}=\sqrt{17-12\sqrt{72}}+\sqrt{17+12\sqrt{72}}=\sqrt{9-2\sqrt{9}.\sqrt{8}+8}+\sqrt{9+2\sqrt{9}.\sqrt{8}+8}=6\)