**
IMPLEMENTATION OF SQUARE ROOT USING VEDIC MATHAMETICS:**

**
DUPLEX METHOD:^{ }**

** ^{ }**The duplex is the square of the central
digit plus double the cross-product of digits equidistant from the center.

A: For perfect squares the duplex and the dividend will get smaller and reach zero after a few steps.

B: For non-perfect squares the decimal value of the square root can be calculated to any precision desired.

— ** Number -> Processing ->
Calculation = Duplex **

5 ==> 5^{2} = 25

27==>2.(2.7)=28

574 ==> 2(5·4) + 7^{2} = 89

2767==>2(2.7)+2(7.6)=112

14213 ==> 2.(1.3)+2(4.1)+4 = 18

406,739 ==> 2(4·9)+ 2(0·3)+ 2(6·7) = 72+0+84 = 156

123,456 ==> 2(1·6)+ 2(2·5)+ 2(3·4) = 12 +20 +24 = 56

** **

**
GROUPING OF NUMBER**

**
Rules:**

· Grouping be done from right hand side taking 2 digit at a time.

· Remaining numbers in last group be either 1(for odd) or(for even)

· Example:

No: 836798087ŕ 8 36 79 80 87 (single digit in last group)

No: 67854693 ŕ 67 85 46 93 (two digit in last group)

**
Placement of decimal point in the result:**

The decimal point must be placed after n/2 or (n+1)/2 digits.

e.g. no. ŕ53163214 and the corresponding square root is 7291.31.

Here the number of digits is eight, so the decimal point is placed after 8/2=4 digits.

** **