Shop mathematics .. by unknow

Author:unknow
Language: eng
Format: epub
Tags: Arithmetic
Publisher: New York [etc.] : McGraw-Hill book company

18'66'24(432 Explanation: First find the largest

number whose square is equal to or

2X40 = 80 JJ 83

2X430 = 860

2

862

9~fiS~ l ess ^an I**, *ke ^ rst P ef iod. This is

4, since 5 2 is more than 18. Write the 4 to the right for the first figure of the root just as the quotient is put down

17 24 in long division. The first figure of

the root is 4. Square the 4 and write 17 24 its square (16) under the first period

(18) and subtract, leaving 2.

Bring down the next period (66) and annex it to the remainder, giving 266 for what is called the dividend. Annex a cipher to the part of the root already found (4) giving 40; then multiply this by 2, making 80, which is called the trial divisor. Set this off to the left. Divide the dividend (266) by the trial divisor (80). We obtain 3, which is probably the next figure of the root. Write this 3 in the root as the second figure and also add it to the trial divisor, giving 83, which is the final divisor. Multiply this by the figure of the root just found (3) giving 249. Subtract this from the dividend (266) leaving 17.

Bring down the next period (24) and annex to the 17, giving a new dividend 1724. Repeat the preceding process as follows: Annex a cipher to the part of the root already found (43) giving 430; and multiply by 2, giving 860, the.trial divisor. Divide the dividend by this divisor and obtain 2 as the next figure of the root. Put this down as the third figure of the root and also add it to the trial divisor, giving 862 as the final divisor. Multiply this by the 2 and obtain 1724, which leaves no remainder when subtracted from the dividend. As there are no more periods in the original number, the root is complete.

77. Square Roots of Mixed Numbers.—If it is required to find the square root of a number composed of a whole number and a decimal, begin at the decimal point and point off periods to right and left. Then find the root as before. Example:

Find the square root of 257.8623 2' 5 7.86' q 23'00(16.058 + , Answer.

20 _6

26

_1 to or less than 2, the first period. Proceeding as

I 57 before, we get 6 for the second figure. After

subtracting the second time (at a) we find that , eg the trial divisor 320 is larger than the dividend 186. In this case, we place a cipher in the root,

annex another cipher to 320 making 3200, annex

the next period, 23, to the dividend and then 1 60 25 proceed as before. If the root proves, as in this

25 98 00 case, to be an interminable decimal (one that

does not end) continue for two or three decimal

5

320.5

32100

8

32108

25 68 64

places and put a + sign after the root as in division. In this example the decimal point comes 29 36 after 16, because there must

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