Solution 3.1:2e - Revision history

Tek at 08:07, 30 September 2008

2008-09-30T08:07:47Z

←Older revision		Revision as of 08:07, 30 September 2008
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-	Looking first at	+	Looking first at <math>\sqrt{18}</math> this square root expression can be simplified by writing 18 as a product of its smallest possible integer factors
-	<math>\sqrt{18}</math>	+
-	this square root expression can be simplified by writing	+
-	~~<math>\text{~~18~~}</math>~~	+
-	as a product of its smallest possible integer factors	+
-		+
-		+
-	~~<math>18=2\centerdot 9=2\centerdot 3\centerdot 3=2\centerdot 3^{2}</math>~~	+

		+	{{Displayed math\|\|<math>18 = 2\cdot 9 = 2\cdot 3\cdot 3 = 2\cdot 3^{2}</math>}}

	and then we can take the quadratic out of the square root sign by using the rule		and then we can take the quadratic out of the square root sign by using the rule
-	<math>\sqrt{a^{2}b}=a\sqrt{b}</math>,	+	<math>\sqrt{a^{2}b}=a\sqrt{b}</math> (valid for non-negative ''a'' and ''b''),

		+	{{Displayed math\|\|<math>\sqrt{18} = \sqrt{2\cdot 3^{2}} = 3\sqrt{2}\,\textrm{.}</math>}}

-	~~<math>\sqrt{18}=\sqrt{2\centerdot 3^{2}}=3\sqrt{2}</math>~~	+	In the same way, we write <math>8 = 2\cdot 4 = 2\cdot 2\cdot 2 = 2^{3}</math> and get
-		+
-	In the same way, we write	+
-	<math>8=2\~~centerdot~~ 4=2\~~centerdot~~ 2\~~centerdot~~ 2=2^{3}</math>	+
-	and get	+
-		+
-		+
-	~~<math>\sqrt{8}=\sqrt{2\centerdot 2^{2}}=2\sqrt{2}</math>~~	+

		+	{{Displayed math\|\|<math>\sqrt{8} = \sqrt{2\cdot 2^{2}} = 2\sqrt{2}\,\textrm{.}</math>}}

	All together, we get		All together, we get

-		+	{{Displayed math\|\|<math>\begin{align}
-	<math>\begin{align}	+	\sqrt{18}\sqrt{8}
-	& \sqrt{18}\sqrt{8}=3\sqrt{2}\~~centerdot~~ 2\sqrt{2}=3\~~centerdot~~ 2\~~centerdot~~ \~~left~~( \sqrt{2} \~~right~~)^{2} \\	+	&= 3\sqrt{2}\cdot 2\sqrt{2}\\[5pt]
-	& =3\~~centerdot~~ 2\~~centerdot~~ 2~~=12~~ \\	+	&= 3\cdot 2\cdot \bigl(\sqrt{2}\bigr)^{2}\\[5pt]
-	& \\	+	&= 3\cdot 2\cdot 2\\[5pt]
-	\end{align}</math>	+	&= 12\,\textrm{.}
		+	\end{align}</math>}}

Ian at 11:01, 22 September 2008

2008-09-22T11:01:20Z

←Older revision		Revision as of 11:01, 22 September 2008
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-	{{~~NAVCONTENT_START~~}}	+	Looking first at
-	<~~center~~> ~~[[Image:3_1_2e.gif]]~~ </~~center~~>	+	<math>\sqrt{18}</math>
-	{{~~NAVCONTENT_STOP~~}}	+	this square root expression can be simplified by writing
		+	<math>\text{18}</math>
		+	as a product of its smallest possible integer factors
		+
		+
		+	<math>18=2\centerdot 9=2\centerdot 3\centerdot 3=2\centerdot 3^{2}</math>
		+
		+
		+	and then we can take the quadratic out of the square root sign by using the rule
		+	<math>\sqrt{a^{2}b}=a\sqrt{b}</math>,
		+
		+
		+	<math>\sqrt{18}=\sqrt{2\centerdot 3^{2}}=3\sqrt{2}</math>
		+
		+	In the same way, we write
		+	<math>8=2\centerdot 4=2\centerdot 2\centerdot 2=2^{3}</math>
		+	and get
		+
		+
		+	<math>\sqrt{8}=\sqrt{2\centerdot 2^{2}}=2\sqrt{2}</math>
		+
		+
		+	All together, we get
		+
		+
		+	<math>\begin{align}
		+	& \sqrt{18}\sqrt{8}=3\sqrt{2}\centerdot 2\sqrt{2}=3\centerdot 2\centerdot \left( \sqrt{2} \right)^{2} \\
		+	& =3\centerdot 2\centerdot 2=12 \\
		+	& \\
		+	\end{align}</math>

Tekbot: Lösning 3.1:2e moved to Solution 3.1:2e: Robot: moved page

2008-09-09T09:08:43Z

Lösning 3.1:2e moved to Solution 3.1:2e: Robot: moved page

←Older revision

Revision as of 09:08, 9 September 2008

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

2008-08-21T06:51:29Z

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

←Older revision		Revision as of 06:51, 21 August 2008
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Oskar: Ny sida: {{NAVCONTENT_START}} Bild:3_1_2e.gif {{NAVCONTENT_STOP}}

2008-04-01T13:49:36Z

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