Vedic Maths

Some tricks of vedic mathematics, essentially for elementary arithmetic.

To find the square of any number ending in 5, multiply the number obtained after deleting 5 from it with a number incremented by one for a number so obtained and place 25 after it. eg: 25^2 = 2*3 25 = 6 25 = 625; 75^2 = 7*8 25 = 56 25 = 5625; 115^2 = 11*12 25 = 132 25 = 13225

To multiply a number by 11, first put down the digit in the units place in the units place for the answer. Then add the digit in the units place with digit in the tens place for the, substitute the units place digit of the number so obtained the for the tens place digit of the answer, and treat the tens place digit as carry for the addition between tens place and hundreds place of the original number. eg: 23*11 = 2 (2+3) 3 = 253; 765*11 = (7+1) (7+6+1) (6+5) 5 = 8415; 29043*11 = (2+1) (2+9) (9+0) (0+4) (4+3) 3 = 319473.
Also taking analogy from above, to multiply a number by 22,33,44... first multiply the number by 11 and by 2,3,4...

To find the square of a number between 26 and 49, first subtract the difference of the number from 50, from itself. Then divide the number so obtained by 2. Now jot down the square of the difference of the number from 50 in the end of the result of division, allowing for only two places ( not more not less ) and treating the hundreds place digit as carry over, if any. eg: 46^2 = (46 - 4)/2 4^2 = 42/2 16 = 2116; 39^2 = (39 - 11)/2 11^2 = 28/2 121 = 1 (4+1) 21 = 1521.
Drawing analogy from above, to find the square of a number from 51 to 74, add the difference instead of subtracting. eg: 56^2 = (56 + 6)/2 6^2 = 62/2 36 = 3136; 70^2 = (70 + 20)/2 20^2 = 90/2 400 = 4 (5+4) 00 = 4900.

To multiply a number by 125, first add 3 zero's at the end of the number, then divide by 8. eg: 394*125 = 394 * (125*8) /8 = 394000/8 = 49250.

To know the remainder when a number is divided by 3 or 9, first add the digits of the number and then divide the sum by 3 or 9 as the case maybe and take the remainder of this division; it gives the same result. eg: to find remainder when 480275996 is divided by 3 - sum of digits = 50 / 3 = 16 2/3, so remainder is 2; for division by 9 : 50/9 = 5 5/9, so remainder is 5.

This above does not even cover the tip of the tip of the iceberg of knowledge that can be gleaned from Vedas.