Rút gọn các biểu thức:
a) \(\left( {2\sqrt 3 + \sqrt 5 } \right)\sqrt 3 - \sqrt {60} \);
b) \(\left( {5\sqrt 2 + 2\sqrt 5 } \right)\sqrt 5 - \sqrt {250} \);
c) \(\left( {\sqrt {28} - \sqrt {12} - \sqrt 7 } \right)\sqrt 7 + 2\sqrt {21} \);
d) \(\left( {\sqrt {99} - \sqrt {18} - \sqrt {11} } \right)\sqrt {11} + 3\sqrt {22} \).
Gợi ý làm bài
\(\eqalign{
& a)\,\left( {2\sqrt 3 + \sqrt 5 } \right)\sqrt 3 - \sqrt {60} \cr
& = 2\sqrt {{3^2}} + \sqrt {15} - \sqrt {4.15} \cr} \)
\( = 6 + \sqrt {15} - 2\sqrt {15} = 6 - \sqrt {15} \)
\(\eqalign{
& b)\,\left( {5\sqrt 2 + 2\sqrt 5 } \right)\sqrt 5 - \sqrt {250} \cr
& = 5\sqrt {10} + 2\sqrt {{5^2}} - \sqrt {25.10} \cr} \)
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\( = 5\sqrt {10} + 10 - 5\sqrt {10} = 10\)
\(\eqalign{
& c)\,\left( {\sqrt {28} - \sqrt {12} - \sqrt 7 } \right)\sqrt 7 + 2\sqrt {21} \cr
& = \left( {\sqrt {4.7} - \sqrt {4.3} - \sqrt 7 } \right)\sqrt 7 + 2\sqrt {21} \cr} \)
\( = \left( {2\sqrt 7 - 2\sqrt 3 - \sqrt 7 } \right)\sqrt 7 + 2\sqrt {21} \)
\( = 2\sqrt {{7^2}} - 2\sqrt {21} - \sqrt {{7^2}} + 2\sqrt {21} \)
\( = 14 - 7 = 7\)
\(\eqalign{
& d)\,\left( {\sqrt {99} - \sqrt {18} - \sqrt {11} } \right)\sqrt {11} + 3\sqrt {22} \cr
& = \left( {\sqrt {9.11} - \sqrt {9.2} - \sqrt {11} } \right)\sqrt {11} + 3\sqrt {22} \cr} \)
\( = \left( {3\sqrt {11} - 3\sqrt 2 - \sqrt {11} } \right)\sqrt {11} + 3\sqrt {22} \)
\( = 3\sqrt {{{11}^2}} - 3\sqrt {22} - \sqrt {{{11}^2}} + 3\sqrt {22} \)
\( = 33 - 11 = 22\)