Tính giá trị hoặc rút gọn các biểu thức a, $\sqrt{m + 2 \sqrt{m - 1} }$ - $\sqrt{m - 2 \sqrt{m - 1} }$ b, $\sqrt{x - 1 - 2\sqrt{x - 2} }$ + $\sqrt{x - 1 + 2\sqrt{x - 2} }$ c, $\sqrt{ 5 - 2\sqrt{ 5x - x^{2}} }$ với 0 $\leq$ x $\leq$ 5 và $\sqrt{x}$ + $\sqrt{5-x}$ = c d, $\sqrt{a + b + c + 2\sqrt{ac + bc}}$ + ,$\sqrt{a + b + c - 2\sqrt{ac + bc}}$

`a, \sqrt{m+2\sqrt{m-1}}-\sqrt{m-2\sqrt{m-1}}`

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

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

`=\sqrt{m-1}+1-\sqrt{m-1}+1`

`=2`

`b,\sqrt{x-1-2\sqrt{x-2}}-\sqrt{x-1+2\sqrt{x-2}}`

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

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

`=\sqrt{x-2}-1-\sqrt{x-2}-1`

`=-2`

`c, \sqrt{5-2\sqrt{5x-x^2}}`

`=\sqrt{(5-x)-2\sqrt{x(5-x)}+x}`

`=\sqrt{(\sqrt{5-x}-\sqrt{x})^2}`

`=\sqrt{x}-\sqrt{5-x}` (vì `\sqrt{x}>\sqrt{5-x}`)

`=c` (vì `\sqrt{x}-\sqrt{5-x}=c`)

`d, \sqrt{a+b+c+2\sqrt{ac+bc}}+\sqrt{a+b+c-2\sqrt{ac+bc}}`

`=\sqrt{(a+b)+c+2\sqrt{c(a+b)}}+\sqrt{(a+b)+c-2\sqrt{c(a+b)}}`

`=\sqrt{(\sqrt{a+b}+\sqrt{c})^2}+\sqrt{(\sqrt{a+b}-\sqrt{c})^2}`

`=\sqrt{a+b}+\sqrt{c}+\sqrt{a+b}-\sqrt{c}`

`=2\sqrt{a+b}`