Treść zadania

Najlepsze rozwiązanie

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  rzbyszek 1.10.2011 (12:34)

  1.
  
  a)
  
  \sqrt {12}= \sqrt {4 \cdot 3}=2 \sqrt 3
  
  \sqrt {28}= \sqrt {4 \cdot 7}=2 \sqrt 7
  
  \sqrt {44}= \sqrt {4 \cdot 11}=2 \sqrt {11}
  
  \sqrt {80}= \sqrt {16 \cdot 5}=4 \sqrt 5
  
  \sqrt { \frac{1}{45}}= \sqrt \frac{1}{9 \cdot 5}= \frac{1}{3 \sqrt 5}= \frac{3 \sqrt 5}{45}= \frac{ \sqrt 5}{15}
  
  \sqrt {20}+ \sqrt {125}=2 \sqrt 5+5 \sqrt 5=7 \sqrt 5
  
  
  b)
  
  \sqrt [3] {24}=\sqrt [3] {8 \cdot 3}=2\sqrt [3] {3}
  
  \sqrt [3] {32}=\sqrt [3] {8 \cdot 4}=2\sqrt [3] {4}
  
  \sqrt [3] {-48}=\sqrt [3] {-8 \cdot 6}=-2\sqrt [3] {6}
  
  \sqrt [3] { \frac{1}{81}}=\sqrt [3] { \frac{1}{27 \cdot 3}}=\frac {3\sqrt [3] {3}}{27}=\frac {\sqrt [3] {3}}{9}
  
  \sqrt [3] {-108}=\sqrt [3] {-27 \cdot 4}=-3\sqrt [3] {4}
  
  \sqrt [3] {135}-\sqrt [3] {-54}=\sqrt [3] {5 \cdot 27}-\sqrt [3] {-27 \cdot 2}=3 \sqrt [3] {5}+3\sqrt [3] {2}
  
  
  2.
  
  3 \sqrt 2= \sqrt {9 \cdot 2}= \sqrt {18}
  
  4 \sqrt 5= \sqrt {16 \cdot 5}= \sqrt {80}
  
  5 \sqrt [3] {11}= \sqrt [3] {125 \cdot 11}=\sqrt [3] {1375}
  
  8 \sqrt 7= \sqrt {64 \cdot 7}= \sqrt {448}
  
  2 \sqrt [3] { \frac{1}{4}}=\sqrt [3] { 8 \cdot \frac{1}{4}}=\sqrt [3] { 2}
  
  4 \sqrt [3] {-2}=\sqrt [3] { 64 \cdot (-2)}=\sqrt [3] {-128}
  
  
  b)
  
  0,2 \sqrt 2= \sqrt {0,04 \cdot 2}= \sqrt {0,08}
  
  0,3 \sqrt 3= \sqrt {0,09 \cdot 3}= \sqrt {0,27}
  
  1,2 \sqrt { \frac{1}{7}}= \sqrt {1,44 \cdot \frac{1}{7}}= \sqrt { \frac{144}{700}}= \sqrt { \frac{36}{175}}
  
  0,1 \sqrt [3] {-6}=\sqrt [3] {0,001 \cdot (-6)}= \sqrt [3] {-0,006}
  
  0,2 \sqrt [3] {5}=\sqrt [3] {0,008 \cdot 5}= \sqrt [3] {0,04}
  

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