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To find the square root of a number without using a calculator
for example to find the square root of 327
first group as 3, 27 . 00, 00, . . .
Start from the leftmost group ' 3 ' .Find the largest positive
integer whose square is just less
than or equal to this 3. here ' 1' is such a number since 12
< 3.
carry the next two digits ' 27 ' down.
now double the number on top ' 1' and write it at the side
now find the greatest positive integer ' ? ' so that
the product (2?) * (?) is less than or equal to 227
for example
20*0 =0
21*1 =21
22*2 = 44
23*3 = 69
24*4 =96
25*5=125
26*6=156
27*7=189
28*8=224 < 227
29*9=261 > 227
so the digit we require in place
of ' ? ' is 8
write it at the top along with the one to get 18
write 28 * 8 = 224 below the 227 and subtract to get 3
carry down the next two digits ' 00'
note that the decimal point has been crossed
as before double the 18 from the top and write 18*2 = 36 on the
side
as before try to guess the greatest digit '?' such that (36?) * (?) is less than or
equal to 300
360*0 = 0 < 300
361*1 = 361 > 300
so ? = 0
put this digit 0 at the top after 18 remember to put the decimal point
also
now carry the next group ' 00 ' down to get 300 00
as before double the 180 to get 360 (ignore the decimal point) and
write 360 at the side
as before try to guess greatest digit '?' so that (360?) *
(?) is less than or equal to 30000
3600*0 = 0
3601*1 = 3601
. . .
. . .
. . .
3607*7 =25249
3608*8 =28864 < 30000
3609*9 =32481 > 30000
thereforre ? = 8
put 8 at the top to get 18.08,
put 3608*8 =28864 below 30000
and subtract to get 1136
now bring down the next group '00' to get 113600
double 1808 to get 3616 to write on the side
try to guess greatest value of ' ? ' so that (3616?)*(?) is less
than
or equal to 113600
36160*0 =0
36161*1 =36161
36162*2 =72324
36163*3 =108489 < 113600
36164*4 =144656 > 113600
therefore ? = 3
continue the process till you have enough accuracy
here square root of 327 is approximately 18.08
Note
the grouping before you start
3567.23522 will be grouped as 35,67 . 23,52,20
567.23522 will
be grouped as 5,67 . 23,52,20
2.3 will be grouped as 2.30,00,00, ...
and so on
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