Solution 3.1:2f
From Förberedande kurs i matematik 1
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The cube root of a number is the same thing as the number raised to the power | The cube root of a number is the same thing as the number raised to the power | ||
| - | + | 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 | |
| - | <math>\sqrt[3]{a}=a^ | + | |
| - | If we therefore write the number | + | |
| - | + | ||
| - | as a product of its smallest possible integer factors | + | |
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| - | + | ||
| - | + | ||
| + | {{Displayed math||<math>8 = 2\cdot 4 = 2\cdot 2\cdot 2 = 2^{3}</math>}} | ||
we see that | we see that | ||
| + | {{Displayed math||<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>}} | ||
| - | <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 3, i.e. <math>\sqrt[3]{5^{3}} = 5\,</math>, <math>\ \sqrt[3]{6^{3}} = 6\,</math> etc. | |
| - | + | ||
| - | <math>\sqrt[3]{5^{3}}=5,\ | + | |
| - | etc. | + | |
Current revision
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.
