x2/1.2=5.62×10-5, x2=6.744×10-5=67.44×10-6, x=8.2122×10-3=0.0082122 approx.
To find √67.44 using a form of division:
Write 67.44 as 67.44 00 00 00.
Nearest square to 67 is 64=82, so write 8 above 67:
8.
67.44 00 00 00
-64
3 44
Now multiply 8 by 20=160 and divide approximately into 344. 344/160 is approximately 2, so add 2 to 160=162 and write 2 next to 8 in the answer.
Now multiply 162 by 2=324 and subtract from 344:
8. 2
67.44 00 00 00
-64
3 44
-3 24
20 00
Next, multiply 82 by 20=1640. This divides into 2000 just once, so 1640+1=1641 and subtract from 2000 and write 1 next to 2 in the answer:
8. 2 1
67.44 00 00 00
-64
3 44
-3 24
20 00
-16 41
3 59 00
20×821=16420; 35900/16420=2 (approx); 16420+2=16422:
8. 2 1 2
67.44 00 00 00
-64
3 44
-3 24
20 00
-16 41
3 59 00
-3 28 44
30 56 00
20×8212=164240. This divides into 305600 only once so the next subtrahend is 164241. However 2×164241=328482 which is closer to 305600, and we can round off the next decimal as 2:
8. 2 1 2 2
67.44 00 00 00
-64
3 44
-3 24
20 00
-16 41
3 59 00
-3 28 44
30 56 00
16 42 41
4 13 59 ...
The process continues indefinitely because the square root is irrational.
Finally we need the square root of 10-6=10-3 (or 0.001). Hence the square root 8.2122×10-3.