Editing Nth root (section)

====Examples====
{{MOS|section|date=April 2022}}

'''Find the square root of 152.2756.'''

         <u>  1  2. 3  4 </u>
     <u> </u>  /
      \/  01 52.27 56          (Results)    (Explanations)
    &nbsp;
          01                   x = 1        10{{sup|0}}·1·0{{sup|0}}·'''1'''{{sup|2}} + 10{{sup|1}}·2·0{{sup|1}}·'''1'''{{sup|1}}     ≤      1   <   10{{sup|0}}·1·0{{sup|0}}·2{{sup|2}}   + 10{{sup|1}}·2·0{{sup|1}}·2{{sup|1}}
         <u> 01 </u>                  y = 1        y = 10{{sup|0}}·1·0{{sup|0}}·1{{sup|2}}   + 10{{sup|1}}·2·0{{sup|1}}·1{{sup|1}}   =  1 +    0   =     '''1'''
          00 52                x = 2        10{{sup|0}}·1·1{{sup|0}}·'''2'''{{sup|2}} + 10{{sup|1}}·2·1{{sup|1}}·'''2'''{{sup|1}}     ≤     52   <   10{{sup|0}}·1·1{{sup|0}}·3{{sup|2}}   + 10{{sup|1}}·2·1{{sup|1}}·3{{sup|1}}
         <u> 00 44 </u>               y = 44       y = 10{{sup|0}}·1·1{{sup|0}}·2{{sup|2}}   + 10{{sup|1}}·2·1{{sup|1}}·2{{sup|1}}   =  4 +   40   =    '''44'''
             08 27             x = 3        10{{sup|0}}·1·12{{sup|0}}·'''3'''{{sup|2}} + 10{{sup|1}}·2·12{{sup|1}}·'''3'''{{sup|1}}   ≤    827   <   10{{sup|0}}·1·12{{sup|0}}·4{{sup|2}}  + 10{{sup|1}}·2·12{{sup|1}}·4{{sup|1}}
            <u> 07 29 </u>            y = 729      y = 10{{sup|0}}·1·12{{sup|0}}·3{{sup|2}}  + 10{{sup|1}}·2·12{{sup|1}}·3{{sup|1}}  =  9 +  720   =   '''729'''
                98 56          x = 4        10{{sup|0}}·1·123{{sup|0}}·'''4'''{{sup|2}} + 10{{sup|1}}·2·123{{sup|1}}·'''4'''{{sup|1}} ≤   9856   <   10{{sup|0}}·1·123{{sup|0}}·5{{sup|2}} + 10{{sup|1}}·2·123{{sup|1}}·5{{sup|1}}
               <u> 98 56 </u>         y = 9856     y = 10{{sup|0}}·1·123{{sup|0}}·4{{sup|2}} + 10{{sup|1}}·2·123{{sup|1}}·4{{sup|1}} = 16 + 9840   =  '''9856'''
                00 00

Algorithm terminates: Answer is 12.34

'''Find the cube root of 4192 truncated to the nearest thousandth.'''

      <u>   1   6.  1   2   4</u>
  <u>3</u>  /
   \/  004 192.000 000 000          (Results)    (Explanations)
    &nbsp;
       004                          x = 1        10{{sup|0}}·1·0{{sup|0}}·'''1'''{{sup|3}}    +  10{{sup|1}}·3·0{{sup|1}}·'''1'''{{sup|2}}   + 10{{sup|2}}·3·0{{sup|2}}·'''1'''{{sup|1}}    ≤          4  <  10{{sup|0}}·1·0{{sup|0}}·2{{sup|3}}     + 10{{sup|1}}·3·0{{sup|1}}·2{{sup|2}}    + 10{{sup|2}}·3·0{{sup|2}}·2{{sup|1}}
      <u> 001 </u>                         y = 1        y = 10{{sup|0}}·1·0{{sup|0}}·1{{sup|3}}   + 10{{sup|1}}·3·0{{sup|1}}·1{{sup|2}}   + 10{{sup|2}}·3·0{{sup|2}}·1{{sup|1}}   =   1 +      0 +          0   =          '''1'''
       003 192                      x = 6        10{{sup|0}}·1·1{{sup|0}}·'''6'''{{sup|3}}    +  10{{sup|1}}·3·1{{sup|1}}·'''6'''{{sup|2}}   + 10{{sup|2}}·3·1{{sup|2}}·'''6'''{{sup|1}}    ≤       3192  <  10{{sup|0}}·1·1{{sup|0}}·7{{sup|3}}     + 10{{sup|1}}·3·1{{sup|1}}·7{{sup|2}}    + 10{{sup|2}}·3·1{{sup|2}}·7{{sup|1}}
      <u> 003 096 </u>                     y = 3096     y = 10{{sup|0}}·1·1{{sup|0}}·6{{sup|3}}   + 10{{sup|1}}·3·1{{sup|1}}·6{{sup|2}}   + 10{{sup|2}}·3·1{{sup|2}}·6{{sup|1}}   = 216 +  1,080 +      1,800   =      '''3,096'''
           096 000                  x = 1        10{{sup|0}}·1·16{{sup|0}}·'''1'''{{sup|3}}   + 10{{sup|1}}·3·16{{sup|1}}·'''1'''{{sup|2}}   + 10{{sup|2}}·3·16{{sup|2}}·'''1'''{{sup|1}}   ≤      96000  <  10{{sup|0}}·1·16{{sup|0}}·2{{sup|3}}   + 10{{sup|1}}·3·16{{sup|1}}·2{{sup|2}}   + 10{{sup|2}}·3·16{{sup|2}}·2{{sup|1}}
          <u> 077 281 </u>                 y = 77281    y = 10{{sup|0}}·1·16{{sup|0}}·1{{sup|3}}  + 10{{sup|1}}·3·16{{sup|1}}·1{{sup|2}}  + 10{{sup|2}}·3·16{{sup|2}}·1{{sup|1}}  =   1 +    480 +     76,800   =     '''77,281'''
           018 719 000              x = 2        10{{sup|0}}·1·161{{sup|0}}·'''2'''{{sup|3}}  + 10{{sup|1}}·3·161{{sup|1}}·'''2'''{{sup|2}}  + 10{{sup|2}}·3·161{{sup|2}}·'''2'''{{sup|1}}  ≤   18719000  <  10{{sup|0}}·1·161{{sup|0}}·3{{sup|3}}  + 10{{sup|1}}·3·161{{sup|1}}·3{{sup|2}}  + 10{{sup|2}}·3·161{{sup|2}}·3{{sup|1}}
              <u> 015 571 928 </u>         y = 15571928 y = 10{{sup|0}}·1·161{{sup|0}}·2{{sup|3}} + 10{{sup|1}}·3·161{{sup|1}}·2{{sup|2}} + 10{{sup|2}}·3·161{{sup|2}}·2{{sup|1}} =   8 + 19,320 + 15,552,600   = '''15,571,928'''
               003 147 072 000      x = 4        10{{sup|0}}·1·1612{{sup|0}}·'''4'''{{sup|3}} + 10{{sup|1}}·3·1612{{sup|1}}·'''4'''{{sup|2}} + 10{{sup|2}}·3·1612{{sup|2}}·'''4'''{{sup|1}} ≤ 3147072000  <  10{{sup|0}}·1·1612{{sup|0}}·5{{sup|3}} + 10{{sup|1}}·3·1612{{sup|1}}·5{{sup|2}} + 10{{sup|2}}·3·1612{{sup|2}}·5{{sup|1}}

The desired precision is achieved. The cube root of 4192 is 16.124...