The 17th Sutra

(A method to calculate square of a number)

Calculate the numbers ‘s’ and ‘m’ for the number whose sq is to be calculated

Special no ‘s’:

Find the last 2 digits of the number ‘no’ whose sq is to be calculated and then map it with ‘s’ using below rules.

a) {00,01,02………23,24} ——> {00,01,02……….23,24}.

Eg. If last 2 digits are 17 then ‘s’ =17.

b) {25,26,27………49,50} ——> {25,24,……………01,00}.

Eg. If last 2 digits are 36 then ‘s’=14.

c) {50,51,52………73,74} ——> {00,01,02……….23,24}.

Eg. If last 2 digits are 74 then ‘s’=24.

d) {75,76,77………99,00} ——> {25,24,……………01,00}.

Eg. If last 2 digits are 82 then ‘s’=18.

A number ‘m’:

‘m’ is mathematically given by ,

‘m’ = int [{ int(‘no’/25)+1}/2]…

eg. Suppose ‘no’ is 527 then ‘m’ for 527 is

‘m’ =int[{int(527/25)+1}/2]

‘m’=int[{int(21.08)+1}/2]

‘m’=int[{21+1}/2]

‘m’=11

To calculate last 2 digits of square:

Last 2 digits =(‘s’*’s’)%100.

i.e. the remainder when ‘s’ squared is divided by 100.

To calculate remaining digits of square:

rem digits =int[(‘s’*’s’)/100]+25’m’*’m’ + ‘s”m’. {for cases a and c}

rem digits =int[(‘s’*’s’)/100]+25’m’*’m’ – ‘s”m’. {for cases b and d}

P.S

If you find int before any bracket then take only the integral part of the expression inside the bracket.

Stay tuned for the proof. A lot more waiting to come from one and only “

VIKAT SHASTRA

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