Bài tập: Rút gọn các biểu thức sau:
1) \(\dfrac{1}{mn^2}\sqrt{\dfrac{m^2n^4}{5}}\left(m< 0;n\ne0\right)\)
2) \(\sqrt{\dfrac{m^4}{9-12m+4m^2}}\left(m< 1,5\right)\)
3) \(\dfrac{a-1}{\sqrt{a}-1}:\sqrt{\dfrac{\left(a-1\right)^4}{a-2\sqrt{a}+1}}\left(0< a< 1\right)\)
4) \(\dfrac{a-b}{\sqrt{a+b}}:\sqrt{\dfrac{\left(a-b\right)^2}{a\left(a+b\right)}}\left(a>b>0\right)\)
`a, 1/(mn^2) . sqrt ((m^2n^4)/5)
`= 1/5`.
`b, sqrt( m^4/(9 - 12 m + 4m^2))`
`= sqrt ((m^2)^2)/(3-2m)^2))`
`= m^2/(3-2m)`
`c, = (a-1)/(sqrt a-1) xx sqrt ((sqrt a -1)/(a-1)^4))`
`= sqrt(1/(a-1)^2)`
`= 1/|a-1|`
`d, (a-b)/(sqrt (a+b)) : sqrt ((a-b)^2/(a(a+b))`
`= (a-b)/(sqrt (a+b)) xx sqrt( (a(a+b))/(a-b)^2)`
`= sqrt (a/(a+b))`.
