• Vorbereitung Klassenarbeit - Reelle Zahlen
  • Christian Leeser
  • 07.03.2023
  • Mathematik
  • 8, 9, 10
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1
Nenne zu die­sen Qua­drat­wur­zeln die Werte.
  • 36\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{36}
  • 144\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{144}
  • 361\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{361}
  • 400\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{400}
  • 25\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{25}
  • 9\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{9}
  • 16\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{16}
  • 121\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{121}
Lösung1
a)  6              e)  5\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \textbf{a)} \; 6 \;\;\;\;\;\;\; \textbf{e)} \;5
b)  12              f)  3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \textbf{b)} \; 12 \;\;\;\;\;\;\; \textbf{f)} \;3
c)  19              g)  4\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \textbf{c)} \; 19 \;\;\;\;\;\;\; \textbf{g)} \;4
d)  20              h)  11\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \textbf{d)} \; 20 \;\;\;\;\;\;\; \textbf{h)} \;11
2
Be­rech­ne die fol­gen­den Werte zu den an­ge­ge­ben Qua­drat­wur­zeln.
  • 1\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{-1}
  • x6\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{x^6}
  • 81\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{81}
  • a4\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{a^4}
Lösung2
a) kann nicht be­rech­net wer­den, da Ra­di­kand ne­ga­tiv.
b) x4x2=x4x2=x4x2=x2x=x3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{x^4 \cdot x^2} = \sqrt{x^4 \cdot x^2}= \sqrt{x^4} \cdot \sqrt{x^2} = x^2 \cdot x = x^3
c) 9
d) a2\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} a^2
3
Be­rech­ne die fol­gen­den Terme.
  • 81256\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{81 \cdot 256}
  • 63+18\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{63 + 18}
  • 1664\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{16} \cdot \sqrt{64}
  • 289324\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{\sqrt{289}}{\sqrt{324}}
  • 400121\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{400} - \sqrt{121}
  • 288144\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{288 - 144}
  • 28\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{2} \cdot \sqrt{8}
  • 25+144\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{25 + 144}
  • 324:36\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{324 : 36}
  • 4936\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{\sqrt{49}}{\sqrt{36}}
Lösung3
a) 144
b) 9
c) 32
d) 1718\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{17}{18}
e) 220
f) 12
g) 4
h) 13
i) 3
j) 76\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{7}{6}
4
Ziehe teil­wei­se die Wur­zel.
  • 120\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{120}
  • 781\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{\frac{7}{81}}
  • 245625\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{\frac{245}{625}}
  • 50\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{50}
  • 125\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{125}
  • 13100\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{\frac{13}{100}}
  • 40\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{40}
  • 1000\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{1000}
Lösung4
a) 230\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 2\sqrt{30}
b) 79\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{\sqrt{7}}{9}
c) 7525\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{7\sqrt{5}}{25}
d) 52\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 5\sqrt{2}
e) 55\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 5\sqrt{5}
f) 1310\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{\sqrt{13}}{10}
g) 210\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 2\sqrt{10}
h)1010\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 10\sqrt{10}
5
Forme die fol­gen­den Qua­drat­wur­zel­ter­me um.
  • 108(7+3)\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{108} \cdot \left(7 + \sqrt{3}\right)
  • b(b+b3)\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{b} \cdot \left(\sqrt{b} + \sqrt{b^3}\right)
  • 2312+1692\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 231\sqrt{2} + 169\sqrt{2}
  • 26751975\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 267\sqrt{5} - 197\sqrt{5}
  • 5(45+620)\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{5} \cdot \left(\sqrt{45} + 6\sqrt{20}\right)
  • 26751975\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 267\sqrt{5} - 197\sqrt{5}
  • 455\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{45} - \sqrt{5}
  • 121x+49y49x\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \sqrt{121x} + \sqrt{49y}-\sqrt{49x}
6
Eine Acker­flä­che von Bauer Hu­bert soll von einer recht­ecki­gen Flä­che in eine qua­dra­ti­sche Flä­che über­führt wer­den. Der Flä­chen­in­halt soll bei bei­den Flä­chen iden­tisch blei­ben.

Das Recht­eck ist 4m breit und 36m lang. Wie lang ist eine Seite des Qua­drats?
Lösung6
Lö­sungs­an­satz: 436=144144=12\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 4 \cdot 36 = 144 \rightarrow \sqrt{144} = 12

Eine Seite ist 12 m lang.
7
Mache den Nen­ner ra­tio­nal.
  • 7913\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{7}{9}\sqrt{13}
  • 1135\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{11}{\sqrt{35}}
  • 1236\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{12}{3\sqrt{6}}
  • 525\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{5}{\sqrt{25}}
  • 36411\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{36}{4\sqrt{11}}
  • 1135\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{11}{\sqrt{35}}
  • 1247\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{12}{4\sqrt{7}}
  • 535\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} \frac{5}{\sqrt{35}}
8
Be­stim­me zu den fol­gen­den qua­dra­ti­schen Glei­chun­gen die Lö­sungs­men­ge.
  • x2+12534=0\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} x^2 + 12534 = 0
  • 3x2240=3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 3x^2 - 240 = 3
  • 4x2321=3\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 4x^2 - 321 = 3
  • 8x2+16=0\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 8x^{2}+16=0
  • x2=225\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} x^{2}=225
  • x2=1\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} x^{2}=1
  • x2=116\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} x^{2}=\frac{1}{16}
  • 5x2245=0\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 5x^{2}-245=0
  • 11x2+110=1221\gdef\cloze#1{{\raisebox{-.05em}{\colorbox{none}{\color{transparent}{\large{$\displaystyle #1$}}}}}} 11x^{2}+110=1221
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