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This is not exactly a homework problem. I was browsing through an old book, "Elementary Algebra for Schools"

by Hall and Knight, first published in England in 1885. The book can be found online at https://archive.org/details/elementaryalgeb00kniggoog . I was studying the process of finding the square root of the polynomial which is a perfect square. I have attached some snapshots from the book here. This process is explained in the file "squareroot" . The files "example1" and "example2" give two examples of using this process. I have understood so far. Now later in the chapter, the author is using this algebraical method to find the square root of the whole numbers which are perfect squares. I have attached some examples in the files "numerical1" and "numerical2".

Now I have question regarding example 2 given in the file numerical2. How did the author get the value of b = 30.

In the algebraical method, its clear that to get the next term in the root, we divide the first term in the remainder with the twice the first term in the root. But in the case of numerical examples, its not clear how he got b = 30 in the example 2 in the file numerical2. If anybody can explain this it would be nice. Since this is an old book, author doesn't explain in great detail. So understanding it is difficult.

Thanks

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# Understanding square root of a polynomial

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