 # VMO J-1 Squaring numbers above a base.

One special application of base multiplication is squaring numbers near a power of 10.

To square a number just above a power of 10, we apply the Vedic word formula, “Whatever the excess, increase by that amount and set-up the square of the excess.”

In our featured example, 122, the excess of 12 over the base 10 is 2. We thus increase 12 by the excess, 2, to get 14 the first part of the answer. Then we set-up the square of the excess, 22, to get 4 the second part. The full product is 144.

132 = 13 + 3 | 32 = 16 | 9 = 169

162 = 16 + 6 | 62 = 22 | 36  = 256 (The base has only 1 zero so only one place is allotted for the second part, the 3 of 36 must be carried to the next column on the left.)

1082 = 108 + 8 | 82 = 116 | 64 = 11,664

1032 = 103 + 3 | 32 = 106 |9 = 10,609 (The base here is 100 so the second part is allotted two places. So, 9 is written as 09.)

1122 = 112 + 12 | 122 = 124|144 = 125|44 = 12, 544  (Here the base also has two zeroes but second part, 144, has two digits; the 1 in 144 will have to be “carried” to the next column on the left.

Exercise J-1: Find the square of the following numbers:

1. 14; 2) 18; 3) 106; 4)109; 5) 112; 6)21; 7) 24; 8) 111; 9) 116; 10) 1001

Answers to Exercise P-1 of the previous post.

1. 156; 2) 238; 3) 270; 4) 10,908; 5) 11,812; 6) 12,096; 7) 12,768; 8)13,028; 9) 1,027,126; 10) 1,434,864

From Prudente, Virgilio, 25 Math Short Cuts, pp 69 -72.