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Chapter 9 - Radicals

Verbose Brief Super-Brief
Radical Indicators
Simple
Index of Radical Root Index Root Index Index
Opening Start Root Start Root Root
Closing End Root End Root End Root
Nested Once
Index of Radical Nested Root Index Nest Root Index Nest Index
Opening Nested Start Root Nest Start Root Nest Root
Closing Nested End Root Nest End Root Nest End Root
Nested Twice
Index of Radical Nested Twice Root Index Nest Twice Root Index Nest Twice Index
Opening Nested Twice Start Root Nest Twice Start Root Nest Twice Root
Closing Nested Twice End Root Nest Twice End Root Nest Twice End Root
Nested Three Times
Index of Radical Nested 3 Root Index Nest 3 Root Index Nest 3 Index
Opening Nested 3 Start Root Nest 3 Start Root Nest 3 Root
Closing Nested 3 End Root Nest 3 End Root Nest 3 End Root
Rule 9.2 - ID: radicals_SIM2
Applies To
Simple Radicals with Index Other Than 2
Description
The radical index indicator is used when the radical index is not implied to be 2.
Example 2radicals_SIM2-02
Example as described below.
verbose
RootIndex n StartRoot x Superscript m Baseline EndRoot equals left-parenthesis RootIndex n StartRoot x EndRoot right-parenthesis Superscript m Baseline equals x Superscript StartFraction m Over n EndFraction Baseline comma x greater-than 0
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brief
RootIndex n StartRoot x Sup m Base EndRoot equals left-p'ren RootIndex n StartRoot x EndRoot right-p'ren Sup m Base equals x Sup StartFrac m Over n EndFrac Base comma x greater-than 0
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superbrief
Index n Root x Sup m Base EndRoot equals L p'ren Index n Root x EndRoot R p'ren Sup m Base equals x Sup Frac m Over n EndFrac Base comma x greater-than 0
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Comment on example 2
Example 3radicals_SIM2-01
Example as described below.
verbose
RootIndex 3 StartRoot x EndRoot equals x Superscript one-third
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brief
RootIndex 3 StartRoot x EndRoot equals x Sup one-third
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superbrief
Index 3 Root x EndRoot equals x Sup one-third
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Comment on example 3
Comment on rule 9.2
Rule 9.3 - ID: radicals_NES1
Applies To
Nested Square Roots and Other Radicals
Description
For square roots and radicals that contain other square roots or radicals, the indicators denote the level of nestedness.
Example 2radicals_NES1-02
Example as described below.
verbose
NestedRootIndex n NestedStartRoot RootIndex m StartRoot x EndRoot NestedEndRoot equals NestedRootIndex m NestedStartRoot RootIndex n StartRoot x EndRoot NestedEndRoot
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brief
NestRootIndex n NestStartRoot RootIndex m StartRoot x EndRoot NestEndRoot equals NestRootIndex m NestStartRoot RootIndex n StartRoot x EndRoot NestEndRoot
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superbrief
NestIndex n NestRoot Index m Root x EndRoot NestEndRoot equals NestIndex m NestRoot Index n Root x EndRoot NestEndRoot
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Comment on example 2
Example 3radicals_NES1-04
Example as described below.
verbose
x Superscript e minus 2 Baseline equals Nested3StartRoot x NestedTwiceRootIndex 3 NestedTwiceStartRoot x NestedRootIndex 4 NestedStartRoot x RootIndex 5 StartRoot x ellipsis EndRoot NestedEndRoot NestedTwiceEndRoot Nested3EndRoot comma x Element-of double-struck upper R
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brief
x Sup e minus 2 Base equals Nest3StartRoot x NestTwiceRootIndex 3 NestTwiceStartRoot x NestRootIndex 4 NestStartRoot x RootIndex 5 StartRoot x ellipsis EndRoot NestEndRoot NestTwiceEndRoot Nest3EndRoot comma x Element-of double-struck upper R
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superbrief
x Sup e minus 2 Base equals Nest3Root x NestTwiceIndex 3 NestTwiceRoot x NestIndex 4 NestRoot x Index 5 Root x ellipsis EndRoot NestEndRoot NestTwiceEndRoot Nest3EndRoot comma x Element-of double-struck upper R
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Comment on example 3
Example 4radicals_NES1-03
Example as described below.
verbose
StartFraction 2 Over pi EndFraction equals StartFraction StartRoot 2 EndRoot Over 2 EndFraction StartFraction NestedStartRoot 2 plus StartRoot 2 EndRoot NestedEndRoot Over 2 EndFraction StartFraction NestedTwiceStartRoot 2 plus NestedStartRoot 2 plus StartRoot 2 EndRoot NestedEndRoot NestedTwiceEndRoot Over 2 EndFraction ellipsis
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brief
StartFrac 2 Over pi EndFrac equals StartFrac StartRoot 2 EndRoot Over 2 EndFrac StartFrac NestStartRoot 2 plus StartRoot 2 EndRoot NestEndRoot Over 2 EndFrac StartFrac NestTwiceStartRoot 2 plus NestStartRoot 2 plus StartRoot 2 EndRoot NestEndRoot NestTwiceEndRoot Over 2 EndFrac ellipsis
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superbrief
Frac 2 Over pi EndFrac equals Frac Root 2 EndRoot Over 2 EndFrac Frac NestRoot 2 plus Root 2 EndRoot NestEndRoot Over 2 EndFrac Frac NestTwiceRoot 2 plus NestRoot 2 plus Root 2 EndRoot NestEndRoot NestTwiceEndRoot Over 2 EndFrac ellipsis
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Comment on example 4
Comment on rule 9.3
Comment on Chapter 9