From Förberedande kurs i matematik 1

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-	{{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>	+	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
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		+	{{Displayed math||<math>8 = 2\cdot 4 = 2\cdot 2\cdot 2 = 2^{3}</math>}}
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		+	we see that
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		+	{{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>}}
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		+	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.

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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.