MathSpeak™ Core Specification

Grammar Rules

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 9.1 - ID: radicals_SIM1

Applies To

Simple Square Roots

Description

Simple radical indicators are used for simple square roots. The indicator for the radical index is not used, since it is implied to be 2.

Example 1 radicals_SIM1-02

Example as described below.
verbose
StartRoot m plus n EndRoot
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brief
StartRoot m plus n EndRoot
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superbrief
Root m plus n EndRoot
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Example 2 radicals_SIM1-01

Example as described below.
verbose
StartRoot 2 EndRoot
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brief
StartRoot 2 EndRoot
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superbrief
Root 2 EndRoot
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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 1 radicals_SIM2-03

Example as described below.
verbose
RootIndex m plus n StartRoot x plus y EndRoot
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brief
RootIndex m plus n StartRoot x plus y EndRoot
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superbrief
Index m plus n Root x plus y EndRoot
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Example 2 radicals_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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Example 3 radicals_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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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 1 radicals_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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Example 2 radicals_NES1-01

Example as described below.
verbose
NestedStartRoot StartRoot x plus 1 EndRoot plus StartRoot y plus 1 EndRoot NestedEndRoot
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brief
NestStartRoot StartRoot x plus 1 EndRoot plus StartRoot y plus 1 EndRoot NestEndRoot
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superbrief
NestRoot Root x plus 1 EndRoot plus Root y plus 1 EndRoot NestEndRoot
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Example 3 radicals_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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Example 4 radicals_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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