________________
Similarly,
Similarly,
3rd square of 'a'
Now square-roots:
nth square of 'a'
1st square-root of 'a'
2nd square root of 'a' 3rd square-root of 'a'
n square-root of 'a'
Cube and Cube-roots :
Cube of cube of 'a' Square root of cube of 'a'
Another example is
Jain Education International
=
=
=
=
Arhat Vacana, 14(2-3), 2002
=
223
a2n
a1/2
a1/22
2nd Vargita-Samvargita of 2
a1/23
a1/20
(a)"
(a3)
= am+n
= am-n
= amn
|||||
= 212
=
Law of Indices
From the above examples and other material available, Acarya Virasena was fully conversant with the laws of Indices :
am x an
a" ÷ a"
(a)
=
=
For Private & Personal Use Only
=
a1/2
227 ÷ 226
= 226
which means 7th varga of 2 divided by 6 varga of 2 gives the 6 varga
of 2.
a1/4
Vargita-Samvargita
There is a great contribution of Acarya Virasena to give the method of Vargita-Samvargita in process of expressing big numbers. This method has been used for raising of a number to its own power. For example:
1 Vargita Samvargita of 2
211
22 = 4
122/221
a1/8
a1/20
a9
a32
3rd Vargita-Sanwargita of 2 = 2P = This method is very easy to express the big number 256256
In connection with this in Dhavala, there is one another operation called
= 256256
81
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