Question

Tính:

\(\left(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\right)^2\)

Answer 1

\(\left(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\right)^2\)

\(=2+\sqrt{3}+2-\sqrt{3}+2\sqrt{\left(2+\sqrt{3}\right)\left(2-\sqrt{3}\right)}\)

\(=4+2\sqrt{4-3}\)

\(=6\)

Answer 2

\(\left(\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\right)^2\)

= \(2+\sqrt{3}+2\left(\sqrt{2+\sqrt{3}}\right)\left(\sqrt{2-\sqrt{3}}\right)+2-\sqrt{3}\)

= \(4+2.\sqrt{4-3}\)

=6