lehrkraefte:blc:miniaufgaben:kw09-2023 [https://fginfo.ksbg.ch Fachgruppe Informatik der KSBG]

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<PRELOAD>
  miniaufgabe.js
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==== 27. Februar 2023 bis 3. März 2023 ====
=== Montag 27. Februar 2023 ===
Schreiben Sie in Normalform. Faktorisierte Zahlen dürfen faktorisiert bleiben.<JS>miniAufgabe("#exowurzelnnormalform1","#solwurzelnnormalform1",
[["$\\displaystyle \\sqrt{1350}$", "$\\displaystyle \\sqrt{1350} = \\sqrt{3^{3} \\cdot 5^{2} \\cdot 2} = 3 \\cdot 5\\sqrt{3 \\cdot 2}$"], ["$\\displaystyle \\sqrt{6750}$", "$\\displaystyle \\sqrt{6750} = \\sqrt{3^{3} \\cdot 5^{3} \\cdot 2} = 3 \\cdot 5\\sqrt{3 \\cdot 5 \\cdot 2}$"], ["$\\displaystyle \\sqrt{2925}$", "$\\displaystyle \\sqrt{2925} = \\sqrt{3^{2} \\cdot 5^{2} \\cdot 13} = 3 \\cdot 5\\sqrt{13}$"], ["$\\displaystyle \\sqrt{2275}$", "$\\displaystyle \\sqrt{2275} = \\sqrt{5^{2} \\cdot 7 \\cdot 13} = 5\\sqrt{7 \\cdot 13}$"], ["$\\displaystyle \\sqrt{33750}$", "$\\displaystyle \\sqrt{33750} = \\sqrt{3^{3} \\cdot 5^{4} \\cdot 2} = 3 \\cdot 5^{2}\\sqrt{3 \\cdot 2}$"], ["$\\displaystyle \\sqrt{1134}$", "$\\displaystyle \\sqrt{1134} = \\sqrt{3^{4} \\cdot 7 \\cdot 2} = 3^{2}\\sqrt{7 \\cdot 2}$"], ["$\\displaystyle \\sqrt{2275}$", "$\\displaystyle \\sqrt{2275} = \\sqrt{5^{2} \\cdot 7 \\cdot 13} = 5\\sqrt{7 \\cdot 13}$"], ["$\\displaystyle \\sqrt{33750}$", "$\\displaystyle \\sqrt{33750} = \\sqrt{3^{3} \\cdot 5^{4} \\cdot 2} = 3 \\cdot 5^{2}\\sqrt{3 \\cdot 2}$"], ["$\\displaystyle \\sqrt{1350}$", "$\\displaystyle \\sqrt{1350} = \\sqrt{3^{3} \\cdot 5^{2} \\cdot 2} = 3 \\cdot 5\\sqrt{3 \\cdot 2}$"], ["$\\displaystyle \\sqrt{8750}$", "$\\displaystyle \\sqrt{8750} = \\sqrt{5^{4} \\cdot 7 \\cdot 2} = 5^{2}\\sqrt{7 \\cdot 2}$"]],
" <hr> ", " <hr> ");
</JS>
<HTML>
<div id="exowurzelnnormalform1"></div>

</HTML>
<hidden Lösungen>

<HTML>
<div id="solwurzelnnormalform1"></div>
<div style='font-size:12px;color:gray;'>ruby normalform-von-wurzeltermen.rb 1</div>
</HTML>

</hidden>

=== Dienstag 28. Februar 2023 ===
Schreiben Sie in Normalform.<JS>miniAufgabe("#exowurzelnnormalform2","#solwurzelnnormalform2",
[["$\\displaystyle \\frac{\\sqrt{21}}{\\sqrt{77}}$", "$\\displaystyle \\frac{\\sqrt{21}}{\\sqrt{77}} = \\sqrt{\\frac{3\\cdot 7}{7 \\cdot 11}} = \\sqrt{\\frac{3}{11}} = \\sqrt{\\frac{3}{11}} \\cdot \\sqrt{\\frac{11}{11}} = \\frac{1}{11} \\sqrt{33}$"], ["$\\displaystyle \\frac{\\sqrt{6}}{\\sqrt{33}}$", "$\\displaystyle \\frac{\\sqrt{6}}{\\sqrt{33}} = \\sqrt{\\frac{2\\cdot 3}{3 \\cdot 11}} = \\sqrt{\\frac{2}{11}} = \\sqrt{\\frac{2}{11}} \\cdot \\sqrt{\\frac{11}{11}} = \\frac{1}{11} \\sqrt{22}$"], ["$\\displaystyle \\frac{\\sqrt{21}}{\\sqrt{14}}$", "$\\displaystyle \\frac{\\sqrt{21}}{\\sqrt{14}} = \\sqrt{\\frac{3\\cdot 7}{7 \\cdot 2}} = \\sqrt{\\frac{3}{2}} = \\sqrt{\\frac{3}{2}} \\cdot \\sqrt{\\frac{2}{2}} = \\frac{1}{2} \\sqrt{6}$"], ["$\\displaystyle \\frac{\\sqrt{15}}{\\sqrt{39}}$", "$\\displaystyle \\frac{\\sqrt{15}}{\\sqrt{39}} = \\sqrt{\\frac{5\\cdot 3}{3 \\cdot 13}} = \\sqrt{\\frac{5}{13}} = \\sqrt{\\frac{5}{13}} \\cdot \\sqrt{\\frac{13}{13}} = \\frac{1}{13} \\sqrt{65}$"], ["$\\displaystyle \\frac{\\sqrt{22}}{\\sqrt{143}}$", "$\\displaystyle \\frac{\\sqrt{22}}{\\sqrt{143}} = \\sqrt{\\frac{2\\cdot 11}{11 \\cdot 13}} = \\sqrt{\\frac{2}{13}} = \\sqrt{\\frac{2}{13}} \\cdot \\sqrt{\\frac{13}{13}} = \\frac{1}{13} \\sqrt{26}$"], ["$\\displaystyle \\frac{\\sqrt{91}}{\\sqrt{143}}$", "$\\displaystyle \\frac{\\sqrt{91}}{\\sqrt{143}} = \\sqrt{\\frac{7\\cdot 13}{13 \\cdot 11}} = \\sqrt{\\frac{7}{11}} = \\sqrt{\\frac{7}{11}} \\cdot \\sqrt{\\frac{11}{11}} = \\frac{1}{11} \\sqrt{77}$"], ["$\\displaystyle \\frac{\\sqrt{14}}{\\sqrt{35}}$", "$\\displaystyle \\frac{\\sqrt{14}}{\\sqrt{35}} = \\sqrt{\\frac{2\\cdot 7}{7 \\cdot 5}} = \\sqrt{\\frac{2}{5}} = \\sqrt{\\frac{2}{5}} \\cdot \\sqrt{\\frac{5}{5}} = \\frac{1}{5} \\sqrt{10}$"], ["$\\displaystyle \\frac{\\sqrt{77}}{\\sqrt{14}}$", "$\\displaystyle \\frac{\\sqrt{77}}{\\sqrt{14}} = \\sqrt{\\frac{11\\cdot 7}{7 \\cdot 2}} = \\sqrt{\\frac{11}{2}} = \\sqrt{\\frac{11}{2}} \\cdot \\sqrt{\\frac{2}{2}} = \\frac{1}{2} \\sqrt{22}$"], ["$\\displaystyle \\frac{\\sqrt{10}}{\\sqrt{26}}$", "$\\displaystyle \\frac{\\sqrt{10}}{\\sqrt{26}} = \\sqrt{\\frac{5\\cdot 2}{2 \\cdot 13}} = \\sqrt{\\frac{5}{13}} = \\sqrt{\\frac{5}{13}} \\cdot \\sqrt{\\frac{13}{13}} = \\frac{1}{13} \\sqrt{65}$"], ["$\\displaystyle \\frac{\\sqrt{15}}{\\sqrt{55}}$", "$\\displaystyle \\frac{\\sqrt{15}}{\\sqrt{55}} = \\sqrt{\\frac{3\\cdot 5}{5 \\cdot 11}} = \\sqrt{\\frac{3}{11}} = \\sqrt{\\frac{3}{11}} \\cdot \\sqrt{\\frac{11}{11}} = \\frac{1}{11} \\sqrt{33}$"]],
" <hr> ", " <hr> ");
</JS>
<HTML>
<div id="exowurzelnnormalform2"></div>

</HTML>
<hidden Lösungen>

<HTML>
<div id="solwurzelnnormalform2"></div>
<div style='font-size:12px;color:gray;'>ruby normalform-von-wurzeltermen.rb 2</div>
</HTML>

</hidden>