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

Answer 1

Please see below.

The reason is that square root depends critically on such pairs . You can find the some of the details at this answer.

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#.
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Answer 2

When finding the square root of a square number, we take pairs of numbers from right to left because each pair corresponds to a part of the square. Starting from the right ensures that we're dealing with the least significant digits first, which simplifies the calculation process. This method follows the principles of place value, allowing us to decompose the square number into smaller manageable parts and determine the square root iteratively. Taking pairs from the left would not align with the place value system and would make the process more complex and less intuitive. Therefore, the convention is to start from the right when finding the square root of a square number.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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