The power of Vedic mathematics
A FEW examples can demonstrate the reach of Krishna Tirtha's work, which contain several patterns of calculations to be used according to the nature of the problem needing to be solved:
To multiply 785 by 362 using the conventional method, you would first multiply by 2, then by 6 and then by 3 and add the three results to get the answer. However, using Tirtha's formulae would enable you to write down the answer immediately as 284170. Remarkably, the formula allows you to write down the answer starting at the left or the right.
To divide 21,011 by 799, the Tirtha method uses just two steps to discover the quotient is 26 and the remainder is 237. Is 5293240096 divisible by 139? Tirtha's formula enables you not to bother carrying out the division, but simply (and correctly) reply, "Yes."
To express 1/49 as a decimal, no actual division is necessary using the Tirtha method and again, the answer can be written beginning from either the left or the right. In this case, the answer is 0.020408163265306122448979591836734693877551, after which comes a recurring decimal. A modern calculator can give the answer upto only 9 digits.
As there are swift methods of multiplication, there are naturally speedy methods of squaring and cubing and of extracting square and cube roots. In one step, Tirtha's method allows you to write the square of 1007 as 1014049 and the cube of 100012 as 1000360043201728. In one step, too, the square root of 25745476 can be determined as 5074 and the cube root of 33076161 as 321.
In explaining how Vedic computational principles work, one must resort to algebra. A few examples illustrate the computational method:
To multiply 92 by 93, the common method is:
92
x 93
276
+ 828
8556
In Vedic maths, the computation would be: the nearest power of 10 to 92 and 93 is 100. Subtract 92 from 100 to get 8 and 93 from 100 to get 7. Multiply 7 and 8 to get 56, which forms the last part of the answer. To get the first part of the answer, take away either 7 from 92 or 8 from 93 to get 85. So, simply by observation, the answer is 8556.
To square 92 by the Vedic method is even simpler: 92 is 8 less than 100. The first part of the answer will be 92 minus 8 = 84. The second part of the answer will be the square of 8 = 64. The answer is 8464. To square 65, increase 6 by 1 to get 7. The first part of the answer will be 6 multiplied by 7 = 42. The second part will be 5 squared = 25. The answer is 4225. The square of 115: 1 more than 11 is 12 and 11 times 12 is 132. The answer is 13225.
Multiplication is easier to explain, but similar principles work equally efficiently for division, decimals and roots.