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 1radicals_SIM1-01

verbose	StartRoot 2 EndRoot
brief	StartRoot 2 EndRoot
superbrief	Root 2 EndRoot

Comment on example 1

Example 2radicals_SIM1-02

verbose	StartRoot m plus n EndRoot
brief	StartRoot m plus n EndRoot
superbrief	Root m plus n EndRoot

Comment on example 2

Comment on rule 9.1

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 1radicals_SIM2-01

verbose	RootIndex 3 StartRoot x EndRoot equals x Superscript one-third
brief	RootIndex 3 StartRoot x EndRoot equals x Sup one-third
superbrief	Index 3 Root x EndRoot equals x Sup one-third

Comment on example 1

Example 2radicals_SIM2-02

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
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
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

Comment on example 2

Example 3radicals_SIM2-03

verbose	RootIndex m plus n StartRoot x plus y EndRoot
brief	RootIndex m plus n StartRoot x plus y EndRoot
superbrief	Index m plus n Root x plus y EndRoot

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 1radicals_NES1-01

verbose	NestedStartRoot StartRoot x plus 1 EndRoot plus StartRoot y plus 1 EndRoot NestedEndRoot
brief	NestStartRoot StartRoot x plus 1 EndRoot plus StartRoot y plus 1 EndRoot NestEndRoot
superbrief	NestRoot Root x plus 1 EndRoot plus Root y plus 1 EndRoot NestEndRoot

Comment on example 1

Example 2radicals_NES1-02

verbose	NestedRootIndex n NestedStartRoot RootIndex m StartRoot x EndRoot NestedEndRoot equals NestedRootIndex m NestedStartRoot RootIndex n StartRoot x EndRoot NestedEndRoot
brief	NestRootIndex n NestStartRoot RootIndex m StartRoot x EndRoot NestEndRoot equals NestRootIndex m NestStartRoot RootIndex n StartRoot x EndRoot NestEndRoot
superbrief	NestIndex n NestRoot Index m Root x EndRoot NestEndRoot equals NestIndex m NestRoot Index n Root x EndRoot NestEndRoot

Comment on example 2

Example 3radicals_NES1-03

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
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
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

Comment on example 3

Example 4radicals_NES1-04

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
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
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

MathSpeak™ Core Specification

Grammar Rules

MathSpeak™ Settings:

Chapter:

Chapter 9 - Radicals