# VMO J-2 Squaring numbers below a base.

Squaring a number below a base is difficult using the conventional methods because usually, large digits are involved but a Vedic Math sub-Sutra or word formula which states that “whatever the deficiency, lessen by that amount and set-up the square of the deficiency” makes it very easy to perform even mentally.

When trying to square 98, our featured example, using the traditional right to left computation, many would struggle with multiplying 8s and 9s and will surely require pencil and paper to perform the calculation.

We can square large numbers just as easily. To find the square of 987, we first notice that it is just 13 below 1,000 and since from VMO J-1, we know that the square of 13 is 169. Therefore **987 ^{2 }= 987-13 | 13^{2} = 974, 169.**

More examples:

**88 ^{2} = 88 – 12 | 12^{2 }= 76 | 144 = 7744 **(base is 100, only two places is allotted for the second part)

**7 ^{2} = 7 – 3 |3^{2} = 4 | 9 = 49**

**6 ^{2} = 6 – 4 | 4^{2} = 2 | 16 = 36**

**979 ^{2} = 979 – 21 | 21^{2} = 958 | 441 = 958, 441**

Exercise J-2 : Find the square of the following numbers mentally.

- 97; 2) 93; 3) 89; 4) 84; 5) 79; 6) 999; 7) 996; 8) 988; 9) 9994; 10) 9898

Answers to exercise P-2:

- 54; 2) 9702; 3) 9114; 4) 8624; 5) 7275; 6) 7656; 7) 6499; 8) 8554; 9) 970,125; 10) 775, 666

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

Suggested readings:

Glover, James, *The Curious Hats of Magical Maths*, Book 2, p 47

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

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