Lösung 3.1:2e

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K (Lösning 3.1:2e moved to Solution 3.1:2e: Robot: moved page)
Zeile 1: Zeile 1:
-
{{NAVCONTENT_START}}
+
Looking first at
-
<center> [[Image:3_1_2e.gif]] </center>
+
<math>\sqrt{18}</math>
-
{{NAVCONTENT_STOP}}
+
this square root expression can be simplified by writing
 +
<math>\text{18}</math>
 +
as a product of its smallest possible integer factors
 +
 
 +
 
 +
<math>18=2\centerdot 9=2\centerdot 3\centerdot 3=2\centerdot 3^{2}</math>
 +
 
 +
 
 +
and then we can take the quadratic out of the square root sign by using the rule
 +
<math>\sqrt{a^{2}b}=a\sqrt{b}</math>,
 +
 
 +
 
 +
<math>\sqrt{18}=\sqrt{2\centerdot 3^{2}}=3\sqrt{2}</math>
 +
 
 +
In the same way, we write
 +
<math>8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3}</math>
 +
and get
 +
 
 +
 
 +
<math>\sqrt{8}=\sqrt{2\centerdot 2^{2}}=2\sqrt{2}</math>
 +
 
 +
 
 +
All together, we get
 +
 
 +
 
 +
<math>\begin{align}
 +
& \sqrt{18}\sqrt{8}=3\sqrt{2}\centerdot 2\sqrt{2}=3\centerdot 2\centerdot \left( \sqrt{2} \right)^{2} \\
 +
& =3\centerdot 2\centerdot 2=12 \\
 +
& \\
 +
\end{align}</math>

Version vom 11:01, 22. Sep. 2008

Looking first at \displaystyle \sqrt{18} this square root expression can be simplified by writing \displaystyle \text{18} as a product of its smallest possible integer factors


\displaystyle 18=2\centerdot 9=2\centerdot 3\centerdot 3=2\centerdot 3^{2}


and then we can take the quadratic out of the square root sign by using the rule \displaystyle \sqrt{a^{2}b}=a\sqrt{b},


\displaystyle \sqrt{18}=\sqrt{2\centerdot 3^{2}}=3\sqrt{2}

In the same way, we write \displaystyle 8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3} and get


\displaystyle \sqrt{8}=\sqrt{2\centerdot 2^{2}}=2\sqrt{2}


All together, we get


\displaystyle \begin{align} & \sqrt{18}\sqrt{8}=3\sqrt{2}\centerdot 2\sqrt{2}=3\centerdot 2\centerdot \left( \sqrt{2} \right)^{2} \\ & =3\centerdot 2\centerdot 2=12 \\ & \\ \end{align}

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_3.1:2e“