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 422 A R I T H ] as many decimal places in the root as you judge neceffary. Examp. I. Required the cube root of 12812904. Cube number 12812904(234 root 8 ill part 1200"} )48i2 refolvend, 2d part 180 > 3d part 9J i divifor 1389 X3 = 4167 produd. ill part 158700) )6459Q4 r^folvend. 2d part 2760v 3d part ' 16 > 2 divifor 161476 X 4=645,904 produft.

[ E T r G K. tor cannot be extrafted without a remainder, reduce the rulgar fraction to a decimal, and then extract the root. III. Extraction of the Biquadrate Root. Rule. Extraft the fquare root of the given number ; and again extraft the fquare root of the root fo found, and the laft of thefe roots is the root fought. Examp. Required the biquadrate root of 5308416. 5308416 (2304(48 root. 4 16 43)130 88)704 129 704 4604) 18416 18416 If, in the firlt extraftion, there happen to be a rePROOF. mainder, continue the operation, by annexing pairs of ciphers, till you have twice as many decimal places in Square 54756 234 the fquare or firll root, as you propofe to have in the 234 234 laft root. 219024 936 IV. Extraction of the root of the fifth power, 164268 702 or furfolid. 109512 468 Rule I. Divide the given number into periods of five figures, find the neareft lefler root of the left-hand Square 54756 Cube 12812904 period, put the figure fo found in the quot, fubtraft its Examp*. II. Required the cube root of 28^. fifth power, and to the remainder bring down the next period for a refolvend. 28.750000(3.06 root. II. Put a--y for the root, and then the furfolid or fifth power will be aaaaa + qaaaay -f- 1 oaaayy -{27 oaayyy + qayyyy yyyyy. Now, aaaaa being already ) 1750000 refolv. 270000") fiibtrafted,. there remains the other five parts ; and to find^, divide by its coefficient, viz. by ^aaaa--oaaayAr~ 5400 V 363 loaayy + ^ayyy + yyyy; that is, try how often qaaaa is contained in the refolvend; and, by the help of the Div. 275436 X 6 — 1652616 prod. quotient-figure, you make up the other four parts of the divifor. 97384 rem. Examp. Required.the furfolid root of 33554432 P R O O F. 38554432(32 root. .3.06. Sq. 9.3636 243 3.06 3.06 ) 9254432 refolv. 4050000 = qaaaa 561816 1836 54OOOO = 1 oaaay 918 280908 36000= loaayy 1200 = sayyy 28.652616 Sq. 9.3636 16 = yyyy 97384 rem. Divifor 4627216X2=9254432 prod. 28.750000 cube. If the cube root of a vulgar fraftion be required, find To) the cube root of the given numerator for a new numerator, and the cube root of the given denominator for a V. Extraction of the root of the fixth. power, .or new denominator. Thus, the cube root of is -f, Iands cube fquared. the cube root of-§-| is ^; and thus the cube root of Rule. Extraft the fquare root of the given number, .(=15*.) is i=2i. But if-tie root of either the numerator ox denomina- and then extraft the cube root of that root, the laftthiis