Aus Online Mathematik Brückenkurs 1

Version vom 09:09, 9. Sep. 2008 (bearbeiten) Tekbot (Diskussion | Beiträge) K (Lösning 3.1:2f moved to Solution 3.1:2f: Robot: moved page) ← Zum vorherigen Versionsunterschied		Version vom 11:11, 22. Sep. 2008 (bearbeiten) (rückgängig) Ian (Diskussion | Beiträge) Zum nächsten Versionsunterschied →
Zeile 1:		Zeile 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.

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Version vom 11:11, 22. Sep. 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.