Question

[Phạm Khánh Huyền]

\(\sqrt{30+12\sqrt{6}}+\sqrt{30-12\sqrt{6}}\)

\(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}\)

Answer 1

[Phạm Lan Hương]

A/đặt A=\(\sqrt{30+12\sqrt{6}}+\sqrt{30-12\sqrt{6}}\)

\(\Leftrightarrow A^2=60+\sqrt{\left(30+12\sqrt{6}\right)\left(30-12\sqrt{6}\right)}\)

=\(60+6=66\)

\(\Leftrightarrow A=\sqrt{66}\)

B/ đặt B=\(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)

\(\Leftrightarrow B^2=8-\sqrt{\left(4+\sqrt{7}\right)\left(4-\sqrt{7}\right)}=5\)

\(\Leftrightarrow B=\sqrt{5}\)

\(\Leftrightarrow B-\sqrt{2}=\sqrt{5}-\sqrt{2}\)

hay \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\) \(-\sqrt{2}=\sqrt{5}-\sqrt{2}\)