Lösung 3.1:2f
Aus Online Mathematik Brückenkurs 1
(Unterschied zwischen Versionen)
K |
K (Robot: Automated text replacement (-{{Displayed math +{{Abgesetzte Formel)) |
||
| Zeile 2: | Zeile 2: | ||
1/3, i.e. <math>\sqrt[3]{a} = a^{1/3}\,\textrm{.}</math> If we therefore write the number 8 as a product of its smallest possible integer factors | 1/3, i.e. <math>\sqrt[3]{a} = a^{1/3}\,\textrm{.}</math> If we therefore write the number 8 as a product of its smallest possible integer factors | ||
| - | {{ | + | {{Abgesetzte Formel||<math>8 = 2\cdot 4 = 2\cdot 2\cdot 2 = 2^{3}</math>}} |
we see that | we see that | ||
| - | {{ | + | {{Abgesetzte Formel||<math>\sqrt[3]{8} = \sqrt[3]{2^{3}} = \bigl(2^{3}\bigr)^{1/3} = 2^{3\cdot\frac{1}{3}} = 2^{1} = 2\,\textrm{.}</math>}} |
Note: Taking the cube root can thus be seen as cancelling the operation of raising a number to the power 3, i.e. <math>\sqrt[3]{5^{3}} = 5\,</math>, <math>\ \sqrt[3]{6^{3}} = 6\,</math> etc. | Note: Taking the cube root can thus be seen as cancelling the operation of raising a number to the power 3, i.e. <math>\sqrt[3]{5^{3}} = 5\,</math>, <math>\ \sqrt[3]{6^{3}} = 6\,</math> etc. | ||
Version vom 08:36, 22. Okt. 2008
The cube root of a number is the same thing as the number raised to the power 1/3, i.e. \displaystyle \sqrt[3]{a} = a^{1/3}\,\textrm{.} If we therefore write the number 8 as a product of its smallest possible integer factors
| \displaystyle 8 = 2\cdot 4 = 2\cdot 2\cdot 2 = 2^{3} |
we see that
| \displaystyle \sqrt[3]{8} = \sqrt[3]{2^{3}} = \bigl(2^{3}\bigr)^{1/3} = 2^{3\cdot\frac{1}{3}} = 2^{1} = 2\,\textrm{.} |
Note: Taking the cube root can thus be seen as cancelling the operation of raising a number to the power 3, i.e. \displaystyle \sqrt[3]{5^{3}} = 5\,, \displaystyle \ \sqrt[3]{6^{3}} = 6\, etc.
