\(A=\sqrt{\left(9\sqrt{2}+2\sqrt{3}\right)^2}-\sqrt{\left(9\sqrt{2}-\sqrt{3}\right)^2}\)
\(=\left|9\sqrt{2}+2\sqrt{3}\right|-\left|9\sqrt{2}-\sqrt{3}\right|\)
\(=9\sqrt{2}+2\sqrt{3}-9\sqrt{2}+\sqrt{3}=3\sqrt{3}\)
Kiểm tra lại đề bài câu B, chỗ \(\sqrt{2+\sqrt{2+2}}\)
Nếu câu B sửa đề thành:
\(B=\sqrt{2+\sqrt{2}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(=\sqrt{2+\sqrt{2}}.\sqrt{\left(2+\sqrt{2+\sqrt{2}}\right)\left(2-\sqrt{2+\sqrt{2}}\right)}\)
\(=\sqrt{2+\sqrt{2}}.\sqrt{4-\left(2+\sqrt{2}\right)}\)
\(=\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2}}\)
\(=\sqrt{\left(2+\sqrt{2}\right)\left(2-\sqrt{2}\right)}\)
\(=\sqrt{4-2}=\sqrt{2}\)