g: \(=\left|\sqrt{6}-1\right|=\sqrt{6}-1\)

h: \(=\left|2\sqrt{3}-1\right|=2\sqrt{3}-1\)

l: \(=\left|2-\sqrt{3}\right|-2=2-\sqrt{3}-2=-\sqrt{3}\)

j: \(=\left|3-\sqrt{6}\right|+\left|2\sqrt{6}-3\right|\)

\(=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)

Bài này chắc rút gọn

\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)

\(=\sqrt{3^2+2.3\sqrt{6}+\left(\sqrt{6}\right)^2}+\sqrt{3^2-2.3.2\sqrt{6}+\left(2\sqrt{6}\right)^2}\)

\(=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(3-2\sqrt{6}\right) ^2}=3-\sqrt{6}+2\sqrt{6}-3\)

\(=\sqrt{6}\)

\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)

\(=\sqrt{9+6-2.3.\sqrt{6}}+\sqrt{9+24-2.3.2\sqrt{6}}\)

\(=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(3-2\sqrt{6}\right)^2}\)

\(=3-\sqrt{6}-3+2\sqrt{6}=\sqrt{6}\)

\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)

\(=\sqrt{15-2.3\sqrt{6}}+\sqrt{33-2.6\sqrt{6}}\)

\(=\sqrt{15-2\sqrt{54}}+\sqrt{33-2\sqrt{216}}\)

\(=\sqrt{9-2\sqrt{6}\sqrt{9}+6}+\sqrt{24-2\sqrt{24}\sqrt{9}+\sqrt{9}}\)

\(=3-\sqrt{6}+\sqrt{24}-3\)

\(=\sqrt{24}-\sqrt{6}\)

\(=\sqrt{6}\)

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

\(=\sqrt{\left(\sqrt{2}\right)^2-2\cdot\sqrt{2}\cdot1+1^2}+\sqrt{\left(2-\sqrt{2}\right)^2}\)

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

\(=\left|\sqrt{2}-1\right|+\left|2-\sqrt{2}\right|\)

\(=\sqrt{2}-1+2-\sqrt{2}\)

\(=1\)

b) \(\sqrt{33-12\sqrt{6}}-\sqrt{\left(5-2\sqrt{6}\right)^2}\)

\(=\sqrt{\left(2\sqrt{6}\right)^2-2\cdot2\sqrt{6}\cdot3+3^2}-\sqrt{\left(5-2\sqrt{6}\right)^2}\)

\(=\sqrt{\left(2\sqrt{6}-3\right)^2}-\sqrt{\left(5-2\sqrt{6}\right)^2}\)

\(=\left|2\sqrt{6}-3\right|-\left|5-2\sqrt{6}\right|\)

\(=2\sqrt{6}-3-5+2\sqrt{6}\)

\(=4\sqrt{6}-8\)

c) \(\sqrt{7-2\sqrt{6}}+\sqrt{15-6\sqrt{6}}\)

\(=\sqrt{\left(\sqrt{6}\right)^2-2\cdot\sqrt{6}\cdot1+1^2}+\sqrt{3^2-2\cdot3\cdot\sqrt{6}+\left(\sqrt{6}\right)^2}\)

\(=\sqrt{\left(\sqrt{6}-1\right)^2}+\sqrt{\left(3-\sqrt{6}\right)^2}\)

\(=\left|\sqrt{6}-1\right|+\left|3-\sqrt{6}\right|\)

\(=\sqrt{6}-1+3-\sqrt{6}\)

\(=2\)

\(a,\sqrt{3-2\sqrt{2}}+\sqrt{\left(2-\sqrt{2}\right)^2}\)

\(=\sqrt{\left(\sqrt{2}\right)^2-2\cdot\sqrt{2}\cdot1+1}+\left|2-\sqrt{2}\right|\)

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

\(=\left|\sqrt{2}-1\right|+2-\sqrt{2}\)

\(=\sqrt{2}-1+2-\sqrt{2}\)

\(=1\)

\(---\)

\(b,\sqrt{33-12\sqrt{6}}-\sqrt{\left(5-2\sqrt{6}\right)^2}\)

\(=\sqrt{\left(2\sqrt{6}\right)^2-2\cdot2\sqrt{6}\cdot3+3^2}-\left|5-2\sqrt{6}\right|\)

\(=\sqrt{\left(2\sqrt{6}-3\right)^2}-5+2\sqrt{6}\)

\(=\left|2\sqrt{6}-3\right|-5+2\sqrt{6}\)

\(=2\sqrt{6}-3-5+2\sqrt{6}\)

\(=4\sqrt{6}-8\)

\(---\)

\(c,\sqrt{7-2\sqrt{6}}+\sqrt{15-6\sqrt{6}}\)

\(=\sqrt{\left(\sqrt{6}\right)^2-2\cdot\sqrt{6}\cdot1+1^2}+\sqrt{\left(\sqrt{6}\right)^2-2\cdot\sqrt{6}\cdot3+3^2}\)

\(=\sqrt{\left(\sqrt{6}-1\right)^2}+\sqrt{\left(\sqrt{6}-3\right)^2}\)

\(=\left|\sqrt{6}-1\right|+\left|\sqrt{6}-3\right|\)

\(=\sqrt{6}-1+3-\sqrt{6}\)

\(=2\)

#\(Toru\)

\(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)

\(=\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(2\sqrt{6}-3\right)^2}\)

\(=3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)

1)
\(=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}.\sqrt{3}+\left(\sqrt{3}\right)^2}\)
\(=\sqrt{\left(\sqrt{11}-\sqrt{3}\right)^2}=\sqrt{11}-\sqrt{3}\)
2)
\(=\sqrt{\left(\sqrt{7}\right)^2-2.\sqrt{7}\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(\sqrt{7}-\sqrt{5}\right)^2}=\sqrt{7}-\sqrt{5}\)
3)
\(=\sqrt{\left(\sqrt{11}\right)^2-2.\sqrt{11}\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(\sqrt{11}-\sqrt{5}\right)}=\sqrt{11}-\sqrt{5}\)
4)
\(=\sqrt{3^2-2.3.\sqrt{5}+\left(\sqrt{5}\right)^2}=\sqrt{\left(3-\sqrt{5}\right)^2}=3-\sqrt{5}\)
5)
\(=\sqrt{3^2-2.3.2\sqrt{2}+\left(2\sqrt{2}\right)^2}=\sqrt{\left(3-2\sqrt{2}\right)^2}=3-2\sqrt{2}\)

 

\(\sqrt{15+6\sqrt{6}}-\sqrt{33-12\sqrt{6}}\)

\(\Leftrightarrow\sqrt{\left(3+\sqrt{6}\right)^2}-\sqrt{\left(2\sqrt{6}-3\right)^2}\)

\(\Leftrightarrow3+\sqrt{6}-2\sqrt{6}+3\)

\(\Leftrightarrow6-\sqrt{6}\)

\(\sqrt{9-6\sqrt{6}+6}+\sqrt{9+6\sqrt{6}+6}\\ =\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{\left(3+\sqrt{6}\right)^2}=6\)

sửa lại lúc  nhìm nhầm 

\(\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{24-12\sqrt{6}+3}\\ =3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)

\(\sqrt{\left(3-\sqrt{6}\right)^2}+\sqrt{24-12\sqrt{6}+3}\\ =3-\sqrt{6}+2\sqrt{6}-3=\sqrt{6}\)

Đây là sửa lại ko phải chứng minh đâu nhé