Question

Thực hiện phép tính:

a) \(\sqrt{3}\left(\sqrt{192}-\sqrt{75}\right)\);                      b) \(\dfrac{-3\sqrt{18}+5\sqrt{50}-\sqrt{128}}{7\sqrt{2}}\).

Answer 1

a) \(\sqrt 3 .\left( {\sqrt {192}  - \sqrt {75} } \right)\)\( = \sqrt 3 .\left( {\sqrt {64.3}  - \sqrt {25.3} } \right)\)\( = \sqrt 3 .\sqrt 3 \left( {\sqrt {64}  - \sqrt {25} } \right)\)\( = 3.\left( {8 - 5} \right)\)\( = 9\)

b) \(\frac{{ - 3\sqrt {18}  + 5\sqrt {50}  - \sqrt {128} }}{{7\sqrt 2 }}\)\( = \frac{{ - 3.\sqrt {9.2}  + 5.\sqrt {25.2}  - \sqrt {64.2} }}{{7\sqrt 2 }}\)\( = \frac{{\sqrt 2 \left( { - 3\sqrt 9  + 5\sqrt {25}  - \sqrt {64} } \right)}}{{7\sqrt 2 }}\)\( = \frac{ - 9 + 25 - 8}{7}\)\( = \frac{8}{7}\)