Category Archives: Sutra

Sutra 10 – Yaavadunam

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:

Sutra 2 – Nikhilam navatascaramam Dasatah

The Sutra means “All from 9 and the last from 10”.  In mathematical terms, this means find complement of a number.  Subtract the number from the nearest power of 10 such as 10, 100, 1000 etc. The power of 10 from which the difference is calculated is called the 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 Base – Number Complement / Nikhilam
7 10 7 – 10 -3
14 10 14   – 10 4
88 100 88 – 100 -122
109 100 109   – 100 9
5200 10000 5200 – 10000 -4800

Exercise:

1)      Find the compliment and the nearest base of the following numbers

a)      45

b)      8

c)      13

d)      8910

e)      98

f)       105

g)      989

h)      99999

i)        1000001

Sutra 1 – Ekadhikena Purvena

The Sutra means “By one more than the previous one”.  In simple words, add 1 to the previous number to obtain the next number.

Example

  • To get 6, Add 1 to the previous number 5 (5 + 1 = 6)
  • To get 26, add 1 to the previous number 25 ( 25 + 1 = 26)

All right, this is straight forward need no brainer. So what’s great about this Sutra? Below are some great usage of this Sutra which makes it amazing.

1)      Square of Number ending with 5 such as 15, 25, 35, 45, 95, 105 etc.

Solution is just two simple steps to be done in mind.

  1. Multiple the number except the last digit (5) with the next number.
  2. Write 25 after the result of 1st step.

Example:

  • Square of   5 =  [0 x (0 + 1)] 25 = [ 0 x 2] 25 = 25
  • Square of 15 =  [1 x (1 + 1)] 25 = [ 1 x 2] 25 = 225
  • Square of 25 =  [1 x (2 + 1)] 25 = [ 2 x 3] 25 = 625
  • Square of 35 =  [3 x (3 + 1)] 25 = [ 3 x 4] 25 = 1225
  • Square of 45 =  [4 x (4 + 1)] 25 = [ 4 x 5] 25 =  2025
  • Square of 55 =  [5 x (5 + 1)] 25 = [ 5 x 6] 25 =  3025
  • Square of 85 =  [8 x (8 + 1)] 25 = [ 8 x 9] 25 =  7225
  • Square of 95 =  [9 x (9 + 1)] 25 = [ 9 x 10] 25 =  9025
  • Square of  125 =  [12 x (12 + 1)] 25 = [ 12 x 13] 25 =  15625
  • Square of  505 =  [50 x (50 + 1)] 25 = [ 50 x 51] 25 =  255025