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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