Lösung 3.1:3c

Aus Online Mathematik Brückenkurs 1

(Unterschied zwischen Versionen)
Wechseln zu: Navigation, Suche
K
Zeile 1: Zeile 1:
-
We start by looking at the one part of the expression,
+
We start by looking at one part of the expression <math>\sqrt{16}</math>. This subexpression can be simplified since <math>16 = 4\cdot 4 = 4^{2}</math> which gives that <math>\sqrt{16} = \sqrt{4^{2}} = 4</math> and the whole expression becomes
-
<math>\sqrt{16}</math>. This root can be simplified since
+
-
<math>16=4\centerdot 4=4^{2}</math>
+
-
which gives that
+
-
<math>\sqrt{16}=\sqrt{4^{2}}=4</math>
+
-
and the whole expression becomes
+
 +
{{Displayed math||<math>\sqrt{16+\sqrt{16}} = \sqrt{16+4} = \sqrt{20}\,\textrm{.}</math>}}
-
<math>\sqrt{16+\sqrt{16}}=\sqrt{16+4}=\sqrt{20}</math>
+
Can <math>\sqrt{20}</math> be simplified? In order to answer this, we split 20 up into integer factors,
 +
{{Displayed math||<math>20 = 2\cdot 10 = 2\cdot 2\cdot 5 = 2^{2}\cdot 5</math>}}
-
Can
+
and see that 20 contains the square <math>2^2</math> as a factor and can therefore be taken outside the root sign,
-
<math>\sqrt{20}</math>
+
-
be simplified? In order to answer this, we split
+
-
<math>\text{2}0</math>
+
-
up into integer factors,
+
-
 
+
{{Displayed math||<math>\sqrt{20} = \sqrt{2^{2}\centerdot 5} = 2\sqrt{5}\,\textrm{.}</math>}}
-
<math>20=2\centerdot 10=2\centerdot 2\centerdot 5=2^{2}\centerdot 5</math>
+
-
 
+
-
 
+
-
and see that
+
-
<math>\text{2}0\text{ }</math>
+
-
contains the square
+
-
<math>\text{2}^{\text{2}}</math>
+
-
as a factor and can therefore be taken outside the root sign,
+
-
 
+
-
 
+
-
<math>\sqrt{20}=\sqrt{2^{2}\centerdot 5}^{2}=2\sqrt{5}</math>
+

Version vom 10:24, 30. Sep. 2008

We start by looking at one part of the expression \displaystyle \sqrt{16}. This subexpression can be simplified since \displaystyle 16 = 4\cdot 4 = 4^{2} which gives that \displaystyle \sqrt{16} = \sqrt{4^{2}} = 4 and the whole expression becomes

Vorlage:Displayed math

Can \displaystyle \sqrt{20} be simplified? In order to answer this, we split 20 up into integer factors,

Vorlage:Displayed math

and see that 20 contains the square \displaystyle 2^2 as a factor and can therefore be taken outside the root sign,

Vorlage:Displayed math

Von „http://wiki.sommarmatte.se/wikis/2009/bridgecourse1-TU-Berlin/index.php/L%C3%B6sung_3.1:3c“