Question

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

Answer 1

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

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

\(=\sqrt{\left(4-3\right)}=1\)

Answer 2

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

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

Answer 3

\(\sqrt{2+\sqrt{3}}\cdot\sqrt{2-\sqrt{3}}=\sqrt{4-3}=1\)