Vedic Duplex Method For Extracting A Square Root
The Vedic duplex method is an ancient Indian method of extracting the square root. It is a variant of the digit by digit method for calculating the square root of a whole or decimal number one digit at a time. The duplex is the square of the central digit plus double the cross-product of digits equidistant from the center. The duplex is computed from the quotient digits (square root digits) computed thus far, but after the initial digits. The duplex is subtracted from the dividend digit prior to the second subtraction for the product of the quotient digit times the divisor digit. For perfect squares the duplex and the dividend will get smaller and reach zero after a few steps. For non-perfect squares the decimal value of the square root can be calculated to any precision desired. However, as the decimal places proliferate, the duplex adjustment gets larger and longer to calculate. The duplex method follows the Vedic ideal for an algorithm, one-line, mental calculation. It is flexible in choosing the first digit group and the divisor. Small divisors are to be avoided by starting with a larger initial group.
In short, to calculate the duplex of a number, double the product of each pair of equidistant digits plus the square of the center digit (of the digits to the right of the colon).
Number => Calculation = Duplex 574 ==> 2(5·4) + 72 = 89 406,739 ==> 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 88,900,777 ==> 2(8·7)+2(8·7)+2(9·7)+2(0·0) = 112+112+126+0 = 350 48329,03711 ==> 2(4·1)+2(8·1)+2(3·7)+2(2·3)+2(9·0)= 8+16+42+12+0 = 78In a square root calculation the quotient digit set increases incrementally for each step.
Number => Calculation = Duplex: 1 ==> 12 = 1 14 ==>2(1·4) = 8 142 ==> 2(1·2) + 42 = 4 + 16 = 20 14,21 ==> 2(1·1) + 2(4·2) = 2 + 16 = 18 14213 ==> 6+8+4 = 18 142,135 ==> 10+24+4 = 38 1421356 ==> 12+40+12+1 = 65 1421,3562 ==> 4+48+20+6 = 78 142,135,623 ==> 6+16+24+10+9 = 65 142,1356,237 ==> 14+24+8+12+30 = 88 142,13562,373 ==> 6+56+12+4+36+25 = 139Read more about this topic: Methods Of Computing Square Roots
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