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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
\(\eqalign{
& a)\,\left( {2\sqrt 3 + \sqrt 5 } \right)\sqrt 3 – \sqrt {60} \cr
& = 2\sqrt {{3^2}} + \sqrt {15} – \sqrt {4.15} \cr} \)
\( = 6 + \sqrt {15} – 2\sqrt {15} = 6 – \sqrt {15} \)
\(\eqalign{
& b)\,\left( {5\sqrt 2 + 2\sqrt 5 } \right)\sqrt 5 – \sqrt {250} \cr
& = 5\sqrt {10} + 2\sqrt {{5^2}} – \sqrt {25.10} \cr} \)
\( = 5\sqrt {10} + 10 – 5\sqrt {10} = 10\)
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\(\eqalign{
& c)\,\left( {\sqrt {28} – \sqrt {12} – \sqrt 7 } \right)\sqrt 7 + 2\sqrt {21} \cr
& = \left( {\sqrt {4.7} – \sqrt {4.3} – \sqrt 7 } \right)\sqrt 7 + 2\sqrt {21} \cr} \)
\( = \left( {2\sqrt 7 – 2\sqrt 3 – \sqrt 7 } \right)\sqrt 7 + 2\sqrt {21} \)
\( = 2\sqrt {{7^2}} – 2\sqrt {21} – \sqrt {{7^2}} + 2\sqrt {21} \)
\( = 14 – 7 = 7\)
\(\eqalign{
& d)\,\left( {\sqrt {99} – \sqrt {18} – \sqrt {11} } \right)\sqrt {11} + 3\sqrt {22} \cr
& = \left( {\sqrt {9.11} – \sqrt {9.2} – \sqrt {11} } \right)\sqrt {11} + 3\sqrt {22} \cr} \)
\( = \left( {3\sqrt {11} – 3\sqrt 2 – \sqrt {11} } \right)\sqrt {11} + 3\sqrt {22} \)
\( = 3\sqrt {{{11}^2}} – 3\sqrt {22} – \sqrt {{{11}^2}} + 3\sqrt {22} \)
\( = 33 – 11 = 22\)