• Wurzelterme
  • anonym
  • 30.06.2020
  • Allgemeine Hochschulreife
  • Mathematik
  • 9
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Um­gang mit Wur­zel­ter­men

1
Er­mitt­le mit Hilfe dei­nes Ta­schen­rech­ners die Werte von fol­gen­den Zah­len:
7+5=\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt {7} + \sqrt{5}=
6+9=\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{6}+\sqrt{9}=
412=\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{4} \cdot \sqrt{12}=
73=\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{7} \cdot \sqrt{3}=
728=\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{7} \cdot \sqrt{28}=
53+33=\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 5 \cdot \sqrt{3} + 3\cdot \sqrt{3}=
49:7=\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{49} : \sqrt{7}=
56:16=\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{56} : \sqrt{16}=
25+49=\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{25} + \sqrt{49}=
2
Ver­su­che auf­grund der in Auf­ga­be 1 ge­fun­de­nen Er­geb­nis­se Re­geln für fol­gen­de Re­chen­ar­ten zu fin­den:
  • a+b\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt {a} + \sqrt {b}
  • ab\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt {a} - \sqrt {b}
  • ab\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt {a} \cdot \sqrt {b}
  • ab\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{\sqrt {a}}{\sqrt {b}}
  • ac+bc\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} a\cdot \sqrt{c} + b\cdot \sqrt {c}
3
Wel­che Werte darf a je­weils an­neh­men, damit man fol­gen­de Terme be­rech­nen kann?
  • a1\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt {a-1}
  • 5+a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{5+a}
  • a2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{a^2}
  • 4a2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{4-a^2 }
  • a29\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{a^2 - 9}
  • 7a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{7 \cdot a}
  • 6a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt {\frac{6}{a}}
  • a5\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt {\frac{a}{-5}}
  • 6a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{-6 \cdot a}
  • a\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{-a}
4
Ver­ein­fa­che so­weit wie mög­lich (ohne Ta­schen­rech­ner!):
  • 28\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt {2} \cdot \sqrt{8}
  • 545\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt {5} \cdot \sqrt{45}
  • 1580\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{\frac{1}{5}} \cdot \sqrt{80}
  • 51180\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{5} \cdot \sqrt{\frac {1}{180}}
  • 0,753\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{0{,}75}\cdot \sqrt{3}