Solution 3.1:2f

From Förberedande kurs i matematik 1

(Difference between revisions)
Jump to: navigation, search
m (Lösning 3.1:2f moved to Solution 3.1:2f: Robot: moved page)
Line 1: Line 1:
-
{{NAVCONTENT_START}}
+
The cube root of a number is the same thing as the number raised to the power
-
<center> [[Image:3_1_2f.gif]] </center>
+
<math>{1}/{3}\;</math>, i.e.
-
{{NAVCONTENT_STOP}}
+
<math>\sqrt[3]{a}=a^{{1}/{3}\;}</math>
 +
If we therefore write the number
 +
<math>\text{8}</math>
 +
as a product of its smallest possible integer factors
 +
 
 +
 
 +
<math>8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3}</math>
 +
 
 +
 
 +
we see that
 +
 
 +
 
 +
<math>\sqrt[3]{8}=\sqrt[3]{2^{3}}=\left( 2^{3} \right)^{{1}/{3}\;}=2^{3\centerdot \frac{1}{3}}=2^{1}=2</math>.
 +
 
 +
NOTE: Taking the cube root can thus be seen as cancelling the operation of raising a number to the power
 +
<math>\text{3}</math>, i.e.
 +
<math>\sqrt[3]{5^{3}}=5,\quad \sqrt[3]{6^{3}}=6</math>
 +
etc.

Revision as of 11:11, 22 September 2008

The cube root of a number is the same thing as the number raised to the power \displaystyle {1}/{3}\;, i.e. \displaystyle \sqrt[3]{a}=a^{{1}/{3}\;} If we therefore write the number \displaystyle \text{8} as a product of its smallest possible integer factors


\displaystyle 8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3}


we see that


\displaystyle \sqrt[3]{8}=\sqrt[3]{2^{3}}=\left( 2^{3} \right)^{{1}/{3}\;}=2^{3\centerdot \frac{1}{3}}=2^{1}=2.

NOTE: Taking the cube root can thus be seen as cancelling the operation of raising a number to the power \displaystyle \text{3}, i.e. \displaystyle \sqrt[3]{5^{3}}=5,\quad \sqrt[3]{6^{3}}=6 etc.

Retrieved from "http://wiki.sommarmatte.se/wikis/2008/bridgecourse1-ImperialCollege/index.php/Solution_3.1:2f"