multiplied by the other part, together with the square 169/10 69 169/10 +3 100 60 9= 3 16910 +3 100 69 It may be further simplified by leaving out unneces- 169|13 1 69 69 The pupil is now in a position to find the square larger numbers, to examine for the square root of such We are now ready to examine for the square root 100% = 10000 90000 [1000ʻ = 1000000] A study of the table will lead to the conclusion that 230* = 52900 240' = 57600 Consequently the square root of (say) 54756 must lie be- 54756 200 Now, had we been seeking the square root of 52900, Then plainly we see how, in finding the square root of + 30} We have yet to find the units digit of the root. But at this point we may say that the root consists of two parts, one 230, and the other to be found, and may proceed as in the earlier case : 54756/200 + 30+4 400 +30 430 +4 12900 704 1856 The work may now be shortened : 54756|234 4 129 1856 After the pupil has been exercised in extracting the roots of numbers expressed by 5 or 6 digits, he will find no difficulty in determining the square roots of such numbers as 547-56, 5-4756, :054756. The extension to numbers expressed by a higher number of digits will be easy, and the need for marking off into periods of two, starting from the decimal point, as well as its full significance, will have been realized by the pupil. Up to this point we have spoken of numbers whose square root can be extracted; it will be next in order to deal with the approximations to square roots—for example, the square root of 2, 5, etc.; but as this involves nothing essentially new it will not be here discussed. We shall conclude this part of the work by calling attention to the extraction of the square root of a fraction. Since In the case of fractions whose denominators are numbers whose roots can not be exactly determined, we should proceed as follows: an artifice the value of which is apparent. Cube Root.—The method of teaching square root has been presented in such detail that very few words will suffice on the subject of cube root. From examples such as 3 = 27 the meaning of cube and cube root will be brought out, and use may be made of the geometrical illustration of the cube. The pupil should commit to memory the following table : |