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Sunday, October 28, 2012

"When You Know Better You Do Better"


Shortcut technique to find square of a Number

a)      The square of a number ending with 5:
If n is the number formed by the preceding digit/s (before the 5), get the product of n and n+1. Then just append 25 (i.e. 5 x 5) to this product.
For example, 75^2:
7 x 8 = 56; therefore solution is 5625.

Another example, 115^2:
11 x 12 = 132; therefore solution is 13225

b)      For other cases
For other cases of squaring, the same shortcut techniques used in multiplication may be utilised. Especially the general-purpose Urdhva Tiryagbhyam (Vertically and Crosswise) formula. To get the square of a number (of two or more digits), simplify by splitting it into at least two parts, a and b.

Thus (a + b) ^2 = a^2 + 2ab + b^2

The solution comprises three parts, neatly fitting the three boxes shown above. Just adjust for excess carry over.
1)      The head: a^2
2)      The middle: crosswise multiplication and doubling a x b x 2
3)      The tail: b^2

Here is a simple example to illustrate this technique.
23^2 = 529
The steps are:
1)      Tail: 3^2 = 9, put it down in the rightmost box
2)      Middle: 2 x 3 x 2 = 12, put down the 2 in the middle box and carry over the 1
3)      Head: 2^2 = 4, plus the 1 carried over, is 5 in the left box.