Tính: \(\displaystyle \left( {{1 \over 2}.\sqrt {{1 \over 2}} - {3 \over 2}.\sqrt 2 + {4 \over 5}.\sqrt {200} } \right):{1 \over 8}\)

* Hướng dẫn giải

\(\eqalign{
& \left( {{1 \over 2}.\sqrt {{1 \over 2}} - {3 \over 2}.\sqrt 2 + {4 \over 5}.\sqrt {200} } \right):{1 \over 8} \cr 
& = \left( {{1 \over 2}\sqrt {{2 \over {{2^2}}}} - {3 \over 2}\sqrt 2 + {4 \over 5}\sqrt {{{10}^2}.2} } \right):{1 \over 8} \cr & = \left( {{1 \over 2}{\sqrt 2 \over 2} - {3 \over 2}\sqrt 2 + \dfrac{4}5.10\sqrt 2 } \right):{1 \over 8} \cr
& = \left( {{1 \over 4}\sqrt 2 - {3 \over 2}\sqrt 2 + 8\sqrt 2 } \right):{1 \over 8} \cr & = \left( {{1 \over 4} - {3 \over 2} + 8 } \right).\sqrt 2:{1 \over 8} \cr
& = {{27} \over 4}\sqrt 2 .8 = 54\sqrt 2 \cr} \)