Solution 3.1:2f - Revision history

Tek at 08:34, 30 September 2008

2008-09-30T08:34:48Z

←Older revision		Revision as of 08:34, 30 September 2008
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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
-	~~<math>{~~1}/{3~~}\;</math>~~, i.e.	+	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^{{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>~~	+

		+	{{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	+	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>\text{~~3~~}</math>~~, i.e.	+
-	<math>\sqrt[3]{5^{3}}=5,\~~quad~~ \sqrt[3]{6^{3}}=6</math>	+
-	etc.	+

2008-09-22T11:11:34Z

←Older revision		Revision as of 11:11, 22 September 2008
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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~~>	+	<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.

2008-09-09T09:09:03Z

←Older revision

Revision as of 09:09, 9 September 2008

2008-08-21T06:51:39Z

Robot: Automated text replacement (-[[Bild: +[[Image:)

2008-04-01T13:50:32Z

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