# 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, **12 ^{2}**, 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,

**2**, to get

^{2}**4**the second part. The full product is

**144**.

13^{2} = 13 + 3 | 3^{2} = 16 | 9 = 169

16^{2} = 16 + 6 | 6^{2 }= 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.)

108^{2} = 108 + 8 | 8^{2} = 116 | 64 = 11,664

103^{2} = 103 + 3 | 3^{2} = 106 |9 = 10,609 (The base here is **100** so the second part is allotted two places. So, **9** is written as **09**.)

112^{2} = 112 + 12 | 12^{2} = 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:

- 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.

- 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.

Suggested readings:

Williams, Kenneth, *Vedic Mathematics Teacher’s Manual (Intermediate Level) *p. 38

IAVM, Inspirational Maths from India, pp 87-88.