\(\left(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\right).\sqrt{2}\)
= \(\sqrt{2}.\sqrt{2-\sqrt{3}}+\sqrt{2}.\sqrt{2+\sqrt{3}}\)
= \(\sqrt{2.\left(2-\sqrt{3}\right)}+\sqrt{2.\left(2+\sqrt{3}\right)}\)
= \(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
= \(\sqrt{3-2\sqrt{3}+1}+\sqrt{3+2\sqrt{3}+1}\)
= \(\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}\)
= \(\sqrt{3}-1+\sqrt{3}+1=2\sqrt{3}\)
\(\left(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\right)\sqrt{2}\)
\(=\sqrt{2.\left(2-\sqrt{3}\right)}+\sqrt{2.\left(2+\sqrt{3}\right)}\)
\(=\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
Chúc bạn học tốt!!!
\(\left(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\right).\sqrt{2}\)
= \(\sqrt{2}.\sqrt{2-\sqrt{3}}+\sqrt{2}.\sqrt{2+\sqrt{3}}\)
= \(\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
= \(\sqrt{1-2\sqrt{3}+3}+\sqrt{1+2\sqrt{3}+3}\)
= \(\sqrt{\left(1-\sqrt{3}\right)^2}+\sqrt{\left(1+\sqrt{3}\right)^2}\)
= \(\sqrt{3}-1+1+\sqrt{3}\)
= 2\(\sqrt{3}\)
