Question

√49-5√96 +√49+√96

Answer 1

Sửa đề: \(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}\)

\(=\sqrt{49-20\sqrt{6}}+\sqrt{49+20\sqrt{6}}\)

\(=\sqrt{49-2\cdot5\cdot2\sqrt{6}}+\sqrt{49+2\cdot5\cdot2\sqrt{6}}\)

\(=\sqrt{\left(5-2\sqrt{6}\right)^2}+\sqrt{\left(5+2\sqrt{6}\right)^2}\)

\(=5-2\sqrt{6}+5+2\sqrt{6}\)

=10

Answer 2

\(\sqrt{49-5\sqrt{96}}+\sqrt{49+5\sqrt{96}}\)

\(=\sqrt{49-20\sqrt{6}}+\sqrt{49+20\sqrt{6}}\)

\(=\sqrt{5^2-2.5.2\sqrt{6}+\left(2\sqrt{6}\right)^2}+\sqrt{5^2+2.5.2\sqrt{6}+\left(2\sqrt{6}\right)^2}\)

\(=\sqrt{\left(5-2\sqrt{6}\right)^2}+\sqrt{\left(5+2\sqrt{6}\right)^2}\)

\(=5-2\sqrt{6}+5+2\sqrt{6}=10\)