Question

Find the square root of $1331$ using repeated subtraction.

Answer 1

$1331-1=1330$

$1330-3=1327$

$1327-5=1322$

$1322-7=1315$

$1315-9=1306$

$1306-11=1295$

$1295-13=1282$

$1282-15=1267$

$1267-17=1250$

$1250-19=1231$

$1231-21=1210$

$1210-23=1187$

$1187-25=1162$

$1162-27=1135$

$1135-29=1106$

$1106-31=1075$

$1075-33=1042$

$1042-35=1007$

$1007-37=970$

$970-39=931$

$931-41=890$

$890-43=847$

$847-45=802$

$802-47=755$

$755-49=706$

$706-51=655$

$655-53=602$

$602-55=547$

$547-57=490$

$490-59=431$

$431-61=370$

$370-63=307$

$307-65=242$

$242-67=175$

$175-69=106$

$106-71=35$

$35-73=-38$

Since, after repeated subration method we did not get the answer as $0$ after the 36th step, we can say that it is not a perfect quare number.

The square root of $1331$ is somewhere between $36$ and $37$.