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Recall that (x+y)^2 is x^2 + 2xy + y^2. Recall that the square root of (x^2 + 2xy + y^2) is x+y.vStarting from the right, group the dividend into pairs of two numbers then begin work on the left-most number or pair.8Double this number -- take the middle number of the row.wUse just the square root rod has from left to right in each row a square (x^2), a double (2x), and the row number (x).Use just the square root rod and find the square, x^2, smaller than or equal to this square. It is found on row x of the square root rod.yUse Napier's rods to create this double number and find the multiples and INCLUDE THE ADDITIONAL X^2 DIGITS ON THE RIGHT. ---------------> -->^7(10)+(2)vAzzolino, Agnes "multiple" %Use n, the number of pairs of digits !in the radicand, to determine thenumber of digits in the root.square number just smaller thanthe left-most 2-digit pair.6th:#Square and double this square root.!Subtract the product from step 2 from the radicand making a "new radicand."!Divide the "new radicand" by the 7th:double to get a quotient.%Take the SQUARE ROOT of this product.$Subtract the product of the quotient8th:&and the double from the "new radicand" to get an even "newer radicand."Take the SQUARE ROOT of the "newer radicand."9th:#Add the SQUARE ROOT from step 3 andthe SQUARE ROOT from step 9.This sum is the SQUARE ROOT of the problem.,Take the SQUARE ROOT of a four digit number./numbers, group digits of the radicand in pairs.*numbers and also to the right with decimal(From the decimal, to the left with whole10th:'Repeat the procedure until the desired ,accuracy is achieved or until the "radicand remainer" is 0.%Compute the product of 10n-1 and the ,Azzolino, Agnes "Multiplication & Division" Work Page ParametersThe work page font is 36 BOLD.The ZOOM is 75%.!References / Resources Resources Azzolino, Agnes "algorithm" @ 2005 at www.mathnstuff.com/math/spoken/here/1words/a/a11.htm -(last modified 2005), visited 10 April 2009. ; 2008 at www.mathnstuff.com/math/algebra/tt15.htm#divide visited 10 April 2009. @ 2005 at www.mathnstuff.com/math/spoken/here/1words/m/m29.htm bWikipedia', Wikimedia Foundation, Inc., "Napier's bones - From Wikipedia, the free encyclopedia" QGNU Free Documentation License at http://en.wikipedia.org/wiki/Napier%27s_bones G(last modified 16 March 2009, at 20:42 (UTC) ), visited 10 April 2009.  Manipulatives @Azzolino, Agnes"napierb.xls - Digital Manipulative Spread Sheet"E 2009 at www.mathnstuff.com/math/spoken/here/2class/60/napierb.xls NAzzolino, Agnes"nbonesD.gif - Big graphic for paper version of Napier's Bones"E 2009 at www.mathnstuff.com/math/spoken/here/2class/60/nbonesD.gif PAzzolino, Agnes"nbonesE.gif - Small graphic for paper version of Napier's Bones"F 2009 at www.mathnstuff.com/math/spoken/here/2class/60/napierb.xls hFor instructions see www.mathnstuff.com/math/spoken/here/2class/60/nbones.htm or resources listed below.Notes 2009, Agnes Azzolinob\! !T#$\&Ae'-( )8*:+ ,N .B cc  +5<i@  dMbP?_*+%MHP DeskJet 830C/832CC od,,LetterDINU"P$2 PSMTJ@HP DeskJet 830C/832CInputBinUPPERRESDLLUniresDLLPSAlignmentFileHPF880ALPSHelpFileHPFDJ200OrientationPORTRAITPaperSizeLETTERResolutionr300x300PMPlainNormalColorMediaTypeSTANDARDColorModeColor24PQNormalHPHTDLLNameHPFIMG50$$$$"d,,??U} } $ } $ } $ } } $ +@@@      *********  ]   [            +\" ++++++++++++++       $F  6 G   !H  )I")))))))))))))) ,J"-------------./ 0K 0000000000001/ 0L 0000000000001 /E"00000000000001/ 0M 0000000000001/ 0N 0222000000001 /""00222000000001/ 0O 0222000000001/ 0N 0222000000001Dl***4(,,44<<4<<4< *!*"*#*$*%*&*'*(*)*** /P" 00000000000001!/ !0Q !0000000000001"/ "0R "0000000000001 #/S"#00000000000001 $/T"$00000000000001 %/U"%00000000000001&/ &0V &0000000000001 '/W"'00000000000001(/ (0X (0000000000001 )/Y")00000000000001*3 *4Z *4444444444445@4<<444<4<4PH0(  >@7  #AZMRN  dMbP?_*+%"??U} $ %} $ &} m &} $ &} m &} +$ &} ,$ %#,      @'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@ '''''''''''''''''''''''''''''@ '''''''''''''''''''''''''''''@ '''''''''''''''''''''''''''''@ '''''''''''''''''''''''''''''@ '''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@'''''''''''''''''''''''''''''@ '''''''''''''''''''''''''''''D lDDDDDDDDDDDDDDDDDDDDDDDDDDDDDDD!"@!'''''''''''''''''''''''''''''@"'''''''''''''''''''''''''''''D  (   V  # 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