Question

what is the square root of 9.3

Answer 1

Step 1: 
 Divide the number (9.3) by 2 to get the first guess for the square root .
 First guess = 9.3/2 = 4.65.

Step 2:
 Divide 9.3 by the previous result. d = 9.3/4.65 = 2.
 Average this value (d) with that of step 1: (2 + 4.65)/2 = 3.325 (new guess).
 Error = new guess - previous value = 4.65 - 3.325 = 1.325.
 1.325 > 0.001. As error > accuracy, we repeat this step again.

Step 3:
 Divide 9.3 by the previous result. d = 9.3/3.325 = 2.7969924812.
 Average this value (d) with that of step 2: (2.7969924812 + 3.325)/2 = 3.0609962406 (new guess).
 Error = new guess - previous value = 3.325 - 3.0609962406 = 0.2640037594.
 0.2640037594 > 0.001. As error > accuracy, we repeat this step again.

Step 4:
 Divide 9.3 by the previous result. d = 9.3/3.0609962406 = 3.0382265344.
 Average this value (d) with that of step 3: (3.0382265344 + 3.0609962406)/2 = 3.0496113875 (new guess).
 Error = new guess - previous value = 3.0609962406 - 3.0496113875 = 0.0113848531.
 0.0113848531 > 0.001. As error > accuracy, we repeat this step again.

Step 5:
 Divide 9.3 by the previous result. d = 9.3/3.0496113875 = 3.0495688854.
 Average this value (d) with that of step 4: (3.0495688854 + 3.0496113875)/2 = 3.0495901365 (new guess).
 Error = new guess - previous value = 3.0496113875 - 3.0495901365 = 0.000021251.
 0.000021251 <= 0.001. As error <= accuracy, we stop the iterations and use 3.0495901365 as the square root.

So, we can say that the square root of 9.3 is 3.0495