Question

While finding root of a square number why we take pairs of number from right, but not left?

Answer 1

Please see below.

Explanation:

The reason is that square root depends critically on such pairs . You can find the some of the details at [this answer.](https://socratic.org/questions/while-finding-root-of-a-square-number-in-dividing-method-why-we-make-double-of-t#389218)

For example, let us consider squares of three digit numbers starting from `1,2,3,4,5,6,7,8,` and `9`.

These will be as follows (here `pq` represent digits in tens and units place):

`(1pq)^2` ranges from `1,00,00` to `3,99,99`

`(2pq)^2` ranges from `4,00,00` to `8,99,99`

`(3pq)^2` ranges from `9,00,00` to `15,99,99`

`(4pq)^2` ranges from `16,00,00` to `24,99,99`

`(5pq)^2` ranges from `25,00,00` to `35,99,99`

`(6pq)^2` ranges from `36,00,00` to `48,99,99`

`(7pq)^2` ranges from `49,00,00` to `63,99,99`

`(8pq)^2` ranges from `64,00,00` to `80,99,99`

`(9pq)^2` ranges from `81,00,00` to `99,99,99`

Now assume a number like `83521`, which is `289^2`

If we make pairs from left and select `83`, we will considering a number starting from `9` and searching for p's and q's and this will make us very much away from the real square root.

But not so, if we make pairs from right and think of a number like `2pq`.