\i:i: BO \\xvii 



To find the square of any number, factor the number as described 



in th- ."ii l>y IWers of 10," pau r e xv. Knter the body of 



:>le with the first factor. and find the corresponding marginal 

 ig ami column heading which will be the iirst three figures 



of tin- square. Interpolate for the fourth flu ^piare the 



;iich makes it 10 -". Multiply together these two 



Example. Desired the square of 34 850. 



34 85-- = (3-485- 1 4 ) 2 = 3-485 2<Io2x4 - 



In the table 3.470 i tin- m-xt >inalli->t valiu- t- .; 485) stands in !: 

 unni i. The tabular dinYivmv is 14, of which cur difference ( = 3.485 3.479=6) 

 IB T * ? , or 0.4 (as may be seen at one* aded 14). 



II. nee 34850.2 = 12. 14'io 8 = 121 400 ooo. 



Example. Desired (o.oo 049 83)2. 



(o.ooo498i) 2 = 4.98 1 2 -lo- 4 * 2 = 24.83-10 8 = 0.0000002483. 



To find the square root of any number, factor it as in the "Nota- 



tion liy Powers of 10." |au .-pt that // must be now an even 



number, while the first factor must have either one or two digits pie- 

 imal point, whichever may l>e necessary, in order to 

 permit a to In* made even. 



Find. then, from the tahle. interpolating if DeceSSary, the >.juan- 

 root of the firs' . and multiply this l>y icr" /J , the s<iuai< 



:<>r; the produet is the desired square root 



Example I > : i the square root of 347.6. 



(347-6)* =(3-476'i' 



In i Me 3.4. column v47)^ = 1.863 



Interpolations by table gives nee = i 



^347.6)* = 1.864- io = 18.64. 



Example. Desired ^875 200. 



V.\ 9.355*i t = 935-5- 



Example. Desired (0.05643) i. 



(5.643'io- 2 )i = 2.376-10' 1 = 0.2376. 



Example. Desired 0.00006 784. 



67.84- lo" 6 = 8. 236-10-* = 0.00 823 6. 



