# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२११

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एतत् पृष्ठम् परिष्कृतम् अस्ति
15
CHAPTER II -- ARITHMETICAL OPERATIONS.

Square Root.

The rule of work in relation to the operation of (extracting) the square root, which is the fourth (of the parikarman operations) is as follows:--

36. From the (number represented by the figures up to the) last odd place (of notation counted from the right), subtract the (highest possible) square number; then multiply the root (of this number) by two, and divide with this (product the number represented by taking into position the figure belonging to) the (next) even place; and then the square of the quotient (so obtained) is to be subtracted from the (number represented by taking into position the figure belonging to the next) odd place. (If it is so continued till the end), the half of the (last) doubled quantity (comes to be ) the resulting square root.

Examples in illustration thereof.

37. O, friend, tell me quickly the roots of the squares of the numbers from 1 to 9, and of 256 and 576.

38. Find out the square root of 6561 and of 65536.

39. What are the square roots of 4294967296 and 622521 ?

40. What are the square roots of 63664441 and 1771561 ?

41. Tell me, friend, after considering well, the square roots of 1296 and 625.

36. To illustrate the rule, the following example is worked out below:--
To extract the square root of 65536
6 | 55 | 36
22 = 4
2 x 2 = 4)25(5
20
55
52 =  25
25 x 2 = 50)303(6
300
36
62 =  36
256 x 2 = 512) 0 (0
0
Square root required == ${\displaystyle {\tfrac {512}{2}}=256}$