Lösung 3.1:4c

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K
Zeile 1: Zeile 1:
Each term in the expression can be simplified by breaking down the number under the root sign into its factors,
Each term in the expression can be simplified by breaking down the number under the root sign into its factors,
 +
{{Displayed math||<math>\begin{align}
 +
50 &= 5\cdot 10 = 5\cdot 5\cdot 2 = 2\cdot 5^{2}\,,\\[5pt]
 +
20 &= 2\cdot 10 = 2\cdot 2\cdot 5 = 2^{2}\cdot 5\,,\\[5pt]
 +
18 &= 2\cdot 9 = 2\cdot 3\cdot 3 = 2\cdot 3^{2}\,,\\[5pt]
 +
80 &= 8\cdot 10 = (2\cdot 4)\cdot (2\cdot 5) = (2\cdot 2\cdot 2)\cdot (2\cdot 5) = 2^{4}\cdot 5\,,
 +
\end{align}</math>}}
-
<math>\begin{align}
+
and then taking the squares out from under the root sign,
-
& 50=5\centerdot 10=5\centerdot 5\centerdot 2=2\centerdot 5^{2} \\
+
-
& 20=2\centerdot 10=2\centerdot 2\centerdot 5=2^{2}\centerdot 5 \\
+
-
& 18=2\centerdot 9=2\centerdot 3\centerdot 3=2\centerdot 3^{2} \\
+
-
& 80=8\centerdot 10=\left( 2\centerdot 4 \right)\centerdot \left( 2\centerdot 5 \right)=\left( 2\centerdot 2\centerdot 2 \right)\centerdot \left( 2\centerdot 5 \right)=2^{4}\centerdot 5 \\
+
-
\end{align}</math>
+
-
 
+
-
and then taking the squares out from under the root sign.
+
-
 
+
-
 
+
-
<math>\begin{align}
+
-
& \sqrt{50}=\sqrt{2\centerdot 5^{2}}=5\sqrt{2} \\
+
-
& \sqrt{20}=\sqrt{2^{2}\centerdot 5}=2\sqrt{5} \\
+
-
& \sqrt{18}=\sqrt{2\centerdot 3^{2}}=3\sqrt{2} \\
+
-
& \sqrt{80}=\sqrt{2^{4}\centerdot 5}=2^{2}\sqrt{5}=4\sqrt{5} \\
+
-
\end{align}</math>
+
 +
{{Displayed math||<math>\begin{align}
 +
\sqrt{50} &= \sqrt{2\cdot 5^2} = 5\sqrt{2}\,,\\
 +
\sqrt{20} &= \sqrt{2^2\cdot 5} = 2\sqrt{5}\,,\\
 +
\sqrt{18} &= \sqrt{2\cdot 3^2} = 3\sqrt{2}\,,\\
 +
\sqrt{80} &= \sqrt{2^4\cdot 5} = 2^{2}\sqrt{5} = 4\sqrt{5}\,\textrm{.}
 +
\end{align}</math>}}
All together, we get
All together, we get
-
 
+
{{Displayed math||<math>\begin{align}
-
<math>\begin{align}
+
\sqrt{50} + 4\sqrt{20} - 3\sqrt{18} - 2\sqrt{80}
-
& \sqrt{50}+4\sqrt{20}-3\sqrt{18}-2\sqrt{80} \\
+
&= 5\sqrt{2} + 4\cdot 2\sqrt{5} - 3\cdot 3\sqrt{2} - 2\cdot 4\sqrt{5}\\[5pt]
-
& =5\sqrt{2}+4\centerdot 2\sqrt{5}-3\centerdot 3\sqrt{2}-2\centerdot 4\sqrt{5} \\
+
&= 5\sqrt{2} + 8\sqrt{5} - 9\sqrt{2} - 8\sqrt{5}\\[5pt]
-
& =5\sqrt{2}+8\sqrt{5}-9\sqrt{2}-8\sqrt{5} \\
+
&= (5-9)\sqrt{2} + (8-8)\sqrt{5} = -4\sqrt{2}\,\textrm{.}
-
& =\left( 5-9 \right)\sqrt{2}+\left( 8-8 \right)\sqrt{5}=-4\sqrt{2} \\
+
\end{align}</math>}}
-
\end{align}</math>
+

Version vom 11:05, 30. Sep. 2008

Each term in the expression can be simplified by breaking down the number under the root sign into its factors,

Vorlage:Displayed math

and then taking the squares out from under the root sign,

Vorlage:Displayed math

All together, we get

Vorlage:Displayed math

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_3.1:4c“