RULE XVRADICALS
Radical (square root)>
 IndexofRadical<
 OrderofRadical
 First inner radical.
 Second inner radical..
 Third inner radical...
 Termination]
§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)
>x+.>x+y.]+z]
(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)
(2)
<3>x^2"+.<3>x^2"+y^2".]+y^2"]
(the cube root of the sum of x squared, the cube root
of x squared plus y squared, and y squared)
verbose semantics 
NestedRootIndex
3 NestedStartRoot
x squared plus RootIndex
3 StartRoot
x squared plus y squared EndRoot
plus y squared NestedEndRoot


(3)
>.<3>x.]] .k <3>.>x.]]
(the square root of the cube root of x equals the cube
root of the square root of x)
verbose semantics 
NestedStartRoot
RootIndex
3 StartRoot
x EndRoot
NestedEndRoot
equals NestedRootIndex
3 NestedStartRoot
StartRoot
x EndRoot
NestedEndRoot


(4)
>x+.>y+..>z..].]]
(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 
NestedTwiceStartRoot
x plus NestedStartRoot
y plus StartRoot
z EndRoot
NestedEndRoot
NestedTwiceEndRoot

