100 REM Nth root
110 X# = 144
120 PRINT "Finding the nth root of"; X#; "to 6 decimal places"
130 PRINT "  x      n        root    x ^ (1 / n)"
140 PRINT "--------------------------------------"
150 FOR I% = 1 TO 8
160  PRINT USING "###   "; X#;
170  PRINT USING "####    "; I%;
180  N% = I%: PREC# = .0000001#: GOSUB 1000
190  PRINT USING "###.######"; NTH.ROOT#;
200  PRINT USING "    ###.######"; X# ^ (1 / I%)
210 NEXT I%
220 END
1000 REM Calculate the N%th root of value X# to stated precision PREC#
1010 REM Result: NTH.ROOT#
1020 X0# = X#
1030 X1# = X# / N% ' initial guess
1040 WHILE ABS(X1# - X0#) > PREC#
1050  X0# = X1#
1060  X1# = ((N% - 1) * X1# + X# / X1# ^ (N% - 1)) / N%
1070 WEND
1080 NTH.ROOT# = X1#
1090 RETURN