Question

M=\(\sqrt{9+4\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)

N=\(\sqrt{7-4\sqrt{3}}-\sqrt{12-6\sqrt{3}}\)

Answer 1

`M=sqrt{9+4sqrt5}-sqrt{6-2sqrt5}`

`=sqrt{(2+sqrt5)^2}-sqrt{(sqrt5-1)^2}`

`=2+sqrt5-(sqrt5-1)`

`=2+sqrt5-sqrt5+1=3`

`N=sqrt{7-4sqrt3}-sqrt{12-6sqrt3}`

`=sqrt{(2-sqrt3)^2}-sqrt{(3-sqrt3)^2}`

`=2-sqrt3-(3-sqrt3)`

`=2-sqrt3-3+sqrt3=-1`

Answer 2

a) Ta có: \(M=\sqrt{9+4\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)

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

\(=3\)

b) Ta có: \(N=\sqrt{7-4\sqrt{3}}-\sqrt{12-6\sqrt{3}}\)

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

=-1