Simplifying Radicals - Revision history

Lila: /* Licensing */

2021-10-21T17:18:19Z

Licensing

Lila: /* Licensing */

2021-10-21T17:15:02Z

Licensing

Lila at 17:14, 21 October 2021

2021-10-21T17:14:36Z

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Lila at 20:24, 30 September 2021

2021-09-30T20:24:47Z

Lila at 22:59, 29 September 2021

2021-09-29T22:59:52Z

Lila: /* Resources and Examples */

2021-09-15T15:21:57Z

Resources and Examples

Lila: Created page with "==Resources and Examples== * [https://courses.lumenlearning.com/boundless-algebra/chapter/radicals/ Introduction to Radicals], Lumen Learning: Boundless Algebra * [https://www..."

2021-09-14T18:25:28Z

Created page with "==Resources and Examples== * [https://courses.lumenlearning.com/boundless-algebra/chapter/radicals/ Introduction to Radicals], Lumen Learning: Boundless Algebra * [https://www..."

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==Resources and Examples==
* [https://courses.lumenlearning.com/boundless-algebra/chapter/radicals/ Introduction to Radicals], Lumen Learning: Boundless Algebra
* [https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/v/simplifying-square-roots-1 Simplifying Square Roots], Khan Academy
* [https://www.mathwords.com/r/radical_rules.htm Useful Radical/Root Rules for Simplification], Mathwords.com
* [https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Advanced_Algebra_(Redden)/05%3A_Radical_Functions_and_Equations/5.02%3A_Simplifying_Radical_Expressions Example Problems of Simplifying Radicals], LibreTexts

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 == Licensing ==
 Content obtained from:
-* [https://en.wikibooks.org/wiki/Arithmetic/Radicals Radicals, Arithmetic, at Wikibooks] under a CC BY-SA license
+* [https://en.wikibooks.org/wiki/Arithmetic/Radicals Radicals, Wikibooks: Arithmetic] under a CC BY-SA license

← Older revision		Revision as of 17:15, 21 October 2021
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	== Licensing ==		== Licensing ==
−	Content obtained from [https://en.wikibooks.org/wiki/Arithmetic/Radicals Radicals, Arithmetic, at Wikibooks] under a CC BY-SA license	+	Content obtained from:
		+	* [https://en.wikibooks.org/wiki/Arithmetic/Radicals Radicals, Arithmetic, at Wikibooks] under a CC BY-SA license

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 Notice that <math>8=2^3</math>. Since the index of the radical is 2, our expression violates convention 4. We can reduce the exponent of the expression under the radical as follows:
 : <math>\frac{\sqrt{8}}{8} = \frac{\sqrt{2^3}}{8} = \frac{\sqrt{2^2\cdot2}}{8} = \frac{2\cdot\sqrt{2}}{8} = \frac{\sqrt{2}}{4}</math>
 ==Resources==

← Older revision		Revision as of 22:59, 29 September 2021
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		+	We will use the following conventions for simplifying expressions involving radicals:
		+	# Given the expression <math>a^\frac{b}{c}</math>, write this as <math>\sqrt[c]{a^b}</math>
		+	# No fractions under the radical sign
		+	# No radicals in the denominator
		+	# The radicand has no exponentiated factors with exponent greater than or equal to the index of the radical
		+
		+	Example: Simplify the expression <math>\left(\frac{1}{8}\right)^\frac{1}{2}</math>
		+	Using convention 1, we rewrite the given expression as
		+	: <math>\left(\frac{1}{8}\right)^\frac{1}{2} = \sqrt[2]{\left(\frac{1}{8}\right)^1} = \sqrt{\frac{1}{8}}</math>
		+	The expression now violates convention 2. To get rid of the fraction in the radical, apply the rule
		+	<math>\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}</math> and simplify the result:
		+	: <math>\sqrt{\frac{1}{8}} = \frac{\sqrt{1}}{\sqrt{8}} = \frac{1}{\sqrt{8}}</math>
		+	The resulting expression violates convention 3. To get rid of the radical in the denominator, multiply by <math>\frac{\sqrt{8}}{\sqrt{8}}</math>:
		+	: <math>\frac{1}{\sqrt{8}} = \frac{1}{\sqrt{8}}\cdot\frac{\sqrt{8}}{\sqrt{8}} = \frac{\sqrt{8}}{8}</math>
		+	Notice that <math>8=2^3</math>. Since the index of the radical is 2, our expression violates convention 4. We can reduce the exponent of the expression under the radical as follows:
		+	: <math>\frac{\sqrt{8}}{8} = \frac{\sqrt{2^3}}{8} = \frac{\sqrt{2^2\cdot2}}{8} = \frac{2\cdot\sqrt{2}}{8} = \frac{\sqrt{2}}{4}</math>
		+
	==Resources==		==Resources==
	* [https://courses.lumenlearning.com/boundless-algebra/chapter/radicals/ Introduction to Radicals], Lumen Learning: Boundless Algebra		* [https://courses.lumenlearning.com/boundless-algebra/chapter/radicals/ Introduction to Radicals], Lumen Learning: Boundless Algebra

@@ Line 1: / Line 1: @@
-==Resources and Examples==
+==Resources==
 * [https://courses.lumenlearning.com/boundless-algebra/chapter/radicals/ Introduction to Radicals], Lumen Learning: Boundless Algebra
 * [https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:rational-exponents-radicals/x2f8bb11595b61c86:simplifying-square-roots/v/simplifying-square-roots-1 Simplifying Square Roots], Khan Academy
 * [https://www.mathwords.com/r/radical_rules.htm Useful Radical/Root Rules for Simplification], Mathwords.com
 * [https://math.libretexts.org/Bookshelves/Algebra/Book%3A_Advanced_Algebra_(Redden)/05%3A_Radical_Functions_and_Equations/5.02%3A_Simplifying_Radical_Expressions Example Problems of Simplifying Radicals], LibreTexts