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Najlepsze rozwiązanie

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  rzbyszek 16.10.2011 (16:25)

  1)
  
  \left( 4\sqrt {8}+ \frac {1}{12}\sqrt {12}- \frac {1}{4}\sqrt {32}\right) \cdot 8\sqrt {32}=\left( 8\sqrt {2}+ \frac {2\sqrt {3}}{12}- \frac {4\sqrt {2}}{4}\right) \cdot 8 \cdot 4\sqrt {2}=
  
  =\left( 7\sqrt {2}+ \frac {\sqrt {3}}{6}\right) \cdot 32\sqrt {2}=448+ \frac {32}{6}\sqrt {6}=448+5 \frac {1}{3}\sqrt {6}
  
  
  2)
  
  (\sqrt [3]{500}-\sqrt [3]{4}) \cdot \sqrt [3]{2}=(5\sqrt [3]{4}-\sqrt [3]{4}) \cdot \sqrt [3]{2}=4\sqrt [3]{2} \cdot \sqrt [3]{2}=4\sqrt [3]{4}
  
  
  3)
  
  \sqrt {3}(\sqrt {75}+\sqrt {48})=\sqrt {3}(5\sqrt {5}+4\sqrt {3}=5\sqrt {15}+12
  
  
  4)
  
  (\sqrt {27}-\sqrt {12}+\sqrt {27}) : \sqrt {3}=(2\sqrt {27}-\sqrt {12}):\sqrt {3}=
  
  =(6\sqrt {3}-2\sqrt {3}):\sqrt {3}=4\sqrt {3}:\sqrt {3}=4
  
  
  5)
  
  (\sqrt {28}=\sqrt {7}-\sqrt {63}):\sqrt {7}=(2\sqrt {7}=\sqrt {7}=3\sqrt {7}):\sqrt {7}=-2\sqrt {7}:\sqrt {7}=-2
  
  
  6)
  
  (\sqrt {20}+\sqrt {5}+\sqrt {125}+\sqrt {45}):\sqrt {5}=(2\sqrt {5}+\sqrt {5}+5\sqrt {5}+3\sqrt {5}):\sqrt {5}=11\sqrt {5}:\sqrt {5}=11
  
  
  7)
  
  (\sqrt [3]{54}-3\sqrt [3]{16}+\sqrt [3]{128}):\sqrt [3]{2}=(3\sqrt [3]{2}-6\sqrt [3]{2}+4\sqrt [3]{2}):\sqrt [3]{2}=\sqrt [3]{2}:\sqrt [3]{2}=1
  
  
  8)
  
  (3\sqrt {0,06}-\sqrt {0,54}+2\sqrt {0,0024}):\sqrt {6}=
  
  =(3\sqrt {6 \cdot 0,01}-\sqrt {6 \cdot 0,09}+2\sqrt {6 \cdot 0,0004}):\sqrt {6}=
  
  =(0,3\sqrt {6}-0,3\sqrt {6}+0,04\sqrt {6}):\sqrt {6}=0,04\sqrt {6}:\sqrt {6}=0,04

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