a: \(A=\left(2\cdot\sqrt{4+\sqrt{6-2\sqrt5}}\right)\cdot\sqrt{10}-\sqrt2\)
\(=\left(2\cdot\sqrt{4+\sqrt{\left(\sqrt5-1\right)^2}}\right)\cdot\sqrt{10}-\sqrt2\)
\(=\left(2\cdot\sqrt{4+\left(\sqrt5-1\right)}\right)\cdot\sqrt2\cdot\sqrt5-\sqrt2\)
\(=\sqrt2\cdot\sqrt2\cdot\sqrt{3+\sqrt5}\cdot\sqrt{10}-\sqrt2\)
\(=\sqrt{20}\cdot\sqrt{6+2\sqrt5}-\sqrt2=\sqrt{20}\left(\sqrt5+1\right)-\sqrt2\)
\(=\sqrt{100}+\sqrt{20}-\sqrt2=10+2\sqrt5-\sqrt2\)
b: \(M=\sqrt{4+\sqrt7}-\sqrt{4-\sqrt7}-\sqrt2\)
\(=\frac{1}{\sqrt2}\left(\sqrt{8+2\sqrt7}-\sqrt{8-2\sqrt7}-2\right)\)
\(=\frac{1}{\sqrt2}\cdot\left(\sqrt{\left(\sqrt7+1\right)^2}-\sqrt{\left(\sqrt7-1\right)^2}-2\right)\)
\(=\frac{1}{\sqrt2}\left(\sqrt7+1-\sqrt7+1-2\right)=0\)
c: \(A=\sqrt{12-6\sqrt3}+\sqrt{21-12\sqrt3}\)
\(=\sqrt{9-2\cdot3\cdot\sqrt3+3}+\sqrt{12-2\cdot2\sqrt3\cdot3+9}\)
\(=\sqrt{\left(3-\sqrt3\right)^2}+\sqrt{\left(2\sqrt3-3\right)^2}=3-\sqrt3+2\sqrt3-3=\sqrt3\)
d:Sửa đề: \(A=\left(\sqrt{20}-\sqrt{45}+3\sqrt5\right)\cdot\sqrt5\)
\(=\left(2\sqrt5-3\sqrt5+3\sqrt5\right)\cdot\sqrt5\)
\(=2\sqrt5\cdot\sqrt5=10\)
Sửa đề: \(B=\sqrt{\left(\sqrt3-1\right)^2}-\sqrt3\)
\(=\left|\sqrt3-1\right|-\sqrt3\)
\(=\sqrt3-1-\sqrt3=-1\)
