Answer: √1.45 = 1.2041594578792
Explanation: Step 1:
Divide the number (1.45) by 2 to get the first guess for the square root .
First guess = 1.45/2 = 0.725.
Step 2:
Divide 1.45 by the previous result. d = 1.45/0.725 = 2.
Average this value (d) with that of step 1: (2 + 0.725)/2 = 1.3625.
previous value = 0.725 - 1.3625 = 0.6375.
0.6375 > 0.001. accuracy, we repeat this step again.
Step 3:
Divide 1.45 by the previous result. d = 1.45/1.3625 = 1.0642201835.
Average this value (d) with that of step 2: (1.0642201835 + 1.3625)/2 = 1.2133600918 .
previous value = 1.3625 - 1.2133600918 = 0.1491399082.
0.1491399082 > 0.001. accuracy, we repeat this step again.
Step 4:
Divide 1.45 by the previous result. d = 1.45/1.2133600918 = 1.1950285903.
Average this value (d) with that of step 3: (1.1950285903 + 1.2133600918)/2 = 1.2041943411.
previous value = 1.2133600918 - 1.2041943411 = 0.0091657507.
0.0091657507 > 0.001. accuracy, we repeat this step again.
Step 5:
Divide 1.45 by the previous result. d = 1.45/1.2041943411 = 1.2041245757.
Average this value (d) with that of step 4: (1.2041245757 + 1.2041943411)/2 = 1.2041594584.
previous value = 1.2041943411 - 1.2041594584 = 0.0000348827.
0.0000348827 <= 0.001. accuracy, we stop the iterations and use 1.2041594584 as the square root.
