पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

10 LOGISTICS
Example. Find the square root of 186624.
Indicating the odd and even places by writing the tachygraphic
abbreviations o and e over the digits, we have
e o e o e o
1 8 6 6 2 4
Subtracting the greatest square number (i.e., 16) from the last
odd place (i.e. from 18), and then setting down double the square root
of 16 underneath the next place, we have
o e o e o
2 6 6 2 4 (remainder)
8 (line of double the square root)
Dividing out 26 by 8 and setting the quotient 3 in the line of double
the square root, we get
e o e o
2 6 2 4 (remainder)
8 3 (line of double the square root)
Subtracting the square of the quotient (i.e., 9) from above, and
doubling the quotient (3), we get
e o e o
1 7 2 4 (remainder)
8 6 (line of double the square root)
One round of the operation is now over. Now we move 86 one place
forward. Then dividing out 172 by 86 and writing the quotient in the
line of double the square root, we get
o e o
4 (remainder)
8 6 2 (line of double the square root)
Finally subtracting the square of the quotient (i.e., 4) from above,
and doubling the quotient 2, we get
o e o
0 (remainder)
8 6 4 (line of double the square root)
The process now ends. So we divide 864 by 2, getting 432 as the
required square root.
As no remainder is left, the square root is exact.