The Sutra means “By the Deficiency”. Here find the deficiency of the number to its nearest base. The difference between the number and the base is termed as deviation or reference base or complement which may be positive or negative.
Example:
Number

Base

Deficiency

8

10

10 – 8 = 2

14

10

10 – 14 = 4

88

100

100 – 88 = 12

109

100

100 – 109 = 9

999

1000

1000 – 999 = 1

99995

100000

100000 – 99995 = 5

Exercise:
1) Find the deficiency of the following numbers to its nearest base
a) 98
b) 7
c) 13
d) 98
e) 105
f) 989
g) 99999
h) 1000001
Square of a number:
Square of a number can be determined by implementing the corollary of this Sutra “Yavadunam Tavadunikrtya Varganca Yojayet”
This means” Whatever is deficiency, subtract it from the number and write the square of that deficiency” This Sutra can be applied to find the square of any number closer to the base of powers of 10. Below are the easy steps.
1) Find the deficiency with the nearest base.
2) Square the deficiency and place at the right side.
3) Subtract the Deficiency from the number
4) Result = [Number – Deficiency + carry over][Square of Deficiency]
Example 1 – Find the Square of 9
1) Base = 10, Deficiency = 1
2) Square of the Deficiency = 1
3) Subtract the Deficiency from Number > 9 – 1 = 8, Carry over = 0
4) Square of 9 is [Number – Deficiency + Carry over][Square of Deficiency] = 81
Example 2 – Find the Square of 14
1) Base = 10, Deficiency = – 4
2) Square of the Deficiency = 16
3) Subtract the Deficiency from Number > 14 – (4) = 18, Carry over =1
4) Square of 9 is [Number – Deficiency + carry over][Square of Deficiency] = 196
Example 3 – Find the Square of 98
1) Base = 100, Deficiency = 2
2) Square of the Deficiency = 04
3) Subtract the Deficiency from Number > 98 – 2 = 96, Carry over =0
4) Square of 9 is [Number – Deficiency + carry over][Square of Deficiency] = 9604
Example 4 – Find the Square of 104
1) Base = 100, Deficiency = – 4
2) Square of the Deficiency = 16
3) Subtract the Deficiency from Number > 104 – (4) = 108, Carry over = 0
4) Square of 9 is [Number – Deficiency + carry over][Square of Deficiency] = 10816
Example 5 – Find the Square of 9997
1) Base = 10000, Deficiency = 3
2) Square of the Deficiency = 0009
3) Subtract the Deficiency from Number > 9997 – 3 = 9994, Carry over =0
4) Square of 9 is [Number – Deficiency + carry over][Square of Deficiency] = 99940009
Exercise
Find the Square of following Numbers
1) 96
2) 6
3) 990
4) 111
5) 102
6) 10003
7) 999995
8) 10000008
9) 12
10) 89
Answers: