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RULE XV--RADICALS

Radical (square root)

verbose

(none)

Radical Indicators

Index-of-Radical

verbose

(none)
Order-of-Radical

First inner radical
Second inner radical
Third inner radical

Termination

verbose

(none)

§103. Simple Radicals: The most commonly occurring radical is the square root.

a. When the square root sign has a vinculum (horizontal bar) which specifies the extent to which the radical sign is effective, the transcription of such a radical is accomplished by the following three steps:

i.The radical symbol >

ii.The expression to which it applies (radicand).

iii.The termination indicator ]

(1)

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(No Nemeth Braille)

verbose semantics

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b. When the square root sign occurs without a radicand, as when attention is being called to a sign in ink print, or when the extent to which the radical is effective is not indicated in ink print by the vinculum, the termination indicator must be omitted.

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(2)

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(No Nemeth Braille)

(no vinculum in ink print)

verbose semantics

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§104. Index of Radical: Radicals of index other than 2 require a specific index. The transcription of such a radical is accomplished by the following three steps:

i. The index-of-radical indicator <

ii. The index of the radical.

iii. Then proceed according to the three steps in §103a.

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§105. Nested Radicals: Occasionally, radicals are nested one within the other. The first inner radical is then regarded as having a depth of order 1, the second inner radical as having a depth of order 2, and so on. In such cases, the order-of-radical indicator (dots 4-6) must be repeated before both the radical symbol and its associated termination indicator as many times as it is necessary to indicate the depth of that radical. If one of the inner radicals is associated with an index, the proper number of order-of-radical indicators must be placed before the index-of-radical indicator rather than before the radical symbol itself. The order-of-radical indicators are provided for the purpose of enabling the reader to keep track of the depth of the radical to which it applies.

(1)

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(No Nemeth Braille)

(the square root of the sum of three terms; the first term is x, the second term is the square root of x plus y; the third term is z)

verbose semantics

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(2)

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(No Nemeth Braille)

(the cube root of the sum of x squared, the cube root of x squared plus y squared, and y squared)

verbose semantics

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(3)

(No image)

(No Nemeth Braille)

(the square root of the cube root of x equals the cube root of the square root of x)

verbose semantics

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(4)

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(No Nemeth Braille)

(a nest of three radicals; the outer radical contains x plus the inner radicals, the first inner radical contains y plus the second inner radical, and the second inner radical contains z)

verbose semantics

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