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Arithmetic Extraction of Square Roots
RATIO  AND  PROPORTION

Engineering Aid 3 - Beginning Structural engineering guide book
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Proceed  as  before  to  determine  the  largest number that can be added as a digit to the divisor 90 and used as a multiplier which, when multiplied by  the  increased  divisor,  will  produce  a  result containable in the remainder, 901. This number is obviously 1. The increased divisor is 901, and this  figure,  multiplied  by  the  1,  gives  a  result exactly equal to the remainder 901. The  figure  1  is  therefore  the  third  and  final digit in the answer, The square root of 2,034.01 is therefore 45.1 Your  completed  computation  appears  thus: Fractional and Negative Exponents In  some  formulas,  like  the  velocity  (V)  of liquids  in  pipes,  which  you  will  encounter  later in Engineering Aid 1 &  C, it is more convenient to  use  FRACTIONAL  EXPONENTS  instead  of radicals. It is readily observed that the index of the root in the above examples is the denominator of the fractional exponent. When an exponent occurs in the  radicand, this   exponent   becomes   the numerator  of  the  fractional  exponent.  Roots  of numbers  not  found  in  tables  may  be  easily computed  by  proper  treatment  of  the  radical  used. Examples: Very   small   or   very   large   numbers   used in science are expressed in the form 5.832  x 10-4 or 8.143  x 106 to  simplify  computation.  To  write out  any  of  these  numbers  in  full,  just  move the  decimal  point  to  either  left  or  right,  the number   of   places   equal   to   the   exponent, supplying a sufficient number of zeros depending upon the sign of the exponent, as shown below: RECIPROCALS The reciprocal of a number is 1 divided by the number. The reciprocal of 2, for example, is 1/2, and  the  reciprocal  of  2/3  is  1  divided  by  2/3, which amounts to 1 x 3/2, or 3/2. The reciprocal of   a   whole   number,   then,   equals   1   over   the number, while the reciprocal of a fraction equals the  fraction  inverted. In  problems  containing  the  power  of  10, generally, it is more convenient to use reciprocals rather than write out lengthy decimals or whole numbers. Example: 1-6







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