पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२१०

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एतत् पृष्ठम् परिष्कृतम् अस्ति
14
GAŅIITASĀRASAŃGRAHA.


31. Get the square of the last figure (in the number, the order of counting the figures being from the right to the left,) and then multiply this last (figure), after it is doubled and pushed on (to the right by on notational place), by (the figures found in) the remaining places. Each of the remaining figures (in the number) is to be pushed on (by one place) and then dealt with similarly. This is the method of squaring.

Examples in illustration thereof.

32. Give out the squares of (the numbers from) 1 to 9, of 15, 16, 25, 36 and 75.

33. What will 338, 4661 and 256 become when squared ?

34. O arithmetician, give out, if you know, the squares of 65536, 12345 and 3333.

35. (Each of the numbers) 6387, and then 7435, and (then) 1022 is squared. O clever arithmetician, tell me, after multiplying well, the value of those three (squares).

Thus ends squaring, the third of the operations known as Parikarman


    31. The pushing on to she right mentioned herein will become clear from the following worked out examples:--

"To square 131. To square 132. To square 555.
12==
2 x 1 x 3==
2 x 1 x 1==
32==
2 x 3 x 1==
12==
    
    
1
6
2
9
6
1
(1)
1 7 1 6 1
12==
2 x 1 x 3==
2 x 1 x 2==
32==
2 x 3 x 2==
22==
    
    
1
6
4
9
12
4
(1) (1)
1 7 4 2 4
52==
2 x 5 x 5==
2 x 5 x 5==
52==
2 x 5 x 5==
52==
    
    
25
50
50
25
50
25
(5) (8) (5) (2)
30 8 0 2 5

    33. Here, 4681 is given as 4000+61+ 600.
    35. Here, 7135 is given as 185+ (1000x7).