### Vedic Math - Squaring numbers near base

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In the previous article, we have discussed about the method of multiplication by using the base value. In this article, we shall learn the squaring of numbers by using base value. Squaring numbers near base is much easier as there is no possibility of different cases that we discussed earlier for multiplication, like
1. One number is above the base and the other number is below it
2. Numbers near different bases like multiplier is near to different base and multiplicand is near to different base.

So it is comparatively simpler. Here, we can use the sub sutra “whatever the extent of its deficiency, lessen it still further to that extent; and also set up the square of that deficiency”.

In this, first corollary is “All from 9 and the last from 10”. This method will work for any type of squaring. There is another method by taking the sutra "Vertically and Crosswise" but that we will discuss later.

Suppose we have to find the square of 8. The following will be the steps for it:
1. We shall take the nearest power of 10 (10 itself in this case) as our base.
2. 8 is '2' lesser than 10, so we shall decrease 2 from 8 (i.e. 8 - 2 = 6). This will become the left side of answer.
3. And, for right part of answer, we write down the square of that deficiency i.e. 2 x 2 = 4
4. Thus 8 x 8 = 64

In exactly the same manner, we say
72 = (7-3)  |  32
=  4  |  9
=  49

92 = (9-1)  |  12
=  8  |  1
=  81

62 = (6-4)  |  42
=  2     |     6                (Here, since right side is 2 digit number, so '1' will be carried to its left)
1
=  3     |   6
=  36