26, đặt bthuc là A suy ra A²=4+4+2\(\sqrt{16-\left(10+2\sqrt{5}\right)}\) suy ra A²=8+2(\(\sqrt{5}\) -1) suy ra A=\(\sqrt{6+2\sqrt{5}}\)=\(\sqrt{5}\)+1

40, tương tự

a) \(E=\sqrt{\left|12\sqrt{5}-29\right|}-\sqrt{12\sqrt{5}+29}\)

\(\Leftrightarrow E^2=\left|12\sqrt{5}-29\right|-12\sqrt{5}-29\)

\(\Leftrightarrow E^2=29-12\sqrt{5}-12\sqrt{5}-29\)

\(\Leftrightarrow E^2=-24\sqrt{5}\)

\(\Leftrightarrow E=-2\sqrt{6\sqrt{5}}\)

b) Đặt \(F=\sqrt{\left|40\sqrt{2}-57\right|}-\sqrt{40\sqrt{2}+57}\)

\(\Leftrightarrow F^2=\left|40\sqrt{2}-57\right|-40\sqrt{2}-57\)

\(\Leftrightarrow F^2=57-40\sqrt{2}-40\sqrt{2}-57\)

\(\Leftrightarrow F^2=-80\sqrt{2}\)

\(\Leftrightarrow F=-4\sqrt{5\sqrt{2}}\)

\(L=0\)

\(L=\sqrt{\left|40\sqrt{2}-57\right|}-\sqrt{\left|40\sqrt{2}-57\right|}\)

\(=\sqrt{40\sqrt{2}-57}-\sqrt{40\sqrt{2}-57}\)

\(=0\)

\(\left(2\sqrt{5}.\sqrt{2}-3\sqrt{40}+\sqrt{90}:3\right):\sqrt{640}=\left(2\sqrt{10}-6\sqrt{10}+\sqrt{10}\right):\left(8\sqrt{10}\right)\)

\(=-\frac{3\sqrt{10}}{8\sqrt{10}}=-\frac{3}{8}\)

1) \(\sqrt{21+12\sqrt{3}}=\sqrt{3^2+2.3.2\sqrt{3}+\left(2\sqrt{3}\right)^2}=\sqrt{\left(3+2\sqrt{3}\right)^2}\)

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

2) \(\sqrt{57-40\sqrt{2}}=\sqrt{5^2-2.5.4\sqrt{2}+\left(4\sqrt{2}\right)^2}=\sqrt{\left(5-4\sqrt{2}\right)^2}\)

                                                                           \(=\left|5-4\sqrt{2}\right|=4\sqrt{2}-5\)

3) \(\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\)

\(=\left|\sqrt{5}+1\right|+\left|\sqrt{5}-1\right|\)

\(=\sqrt{5}+1+\sqrt{5}-1\)

\(=2\sqrt{5}\)

\(=-10\)

\(=-6\)