Question

find the square root of 99/ 209​

Answer 1

Answer:

Since 102=100 and 9.92=98.01 , in between we must have that 9.952≈99.005 .

No, wait! I actually know the exact square of that:

9.952=99.52102=100×99+0.25102 =99.0025

To correct for the remaining error factor of 99.0025/99≈1.000025 , we should reduce our first attempt ( 9.95 ) with the square root of that error factor:

1.000025−−−−−−−√≈1+0.000025/2=1.0000125

Now we can use that

9.951+0.0000125≈9.95×(1−0.0000125)≈9.95−0.000125=9.949875