the square root of 63100 is 251.1971
Step-by-step explanation:
Step 1:
Divide the number (63100) by 2 to get the first guess for the square root .
First guess = 63100/2 = 31550.
Step 2:
Divide 63100 by the previous result. d = 63100/31550 = 2.
Average this value (d) with that of step 1: (2 + 31550)/2 = 15776 (new guess).
Error = new guess - previous value = 31550 - 15776 = 15774.
15774 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 63100 by the previous result. d = 63100/15776 = 3.9997464503.
Average this value (d) with that of step 2: (3.9997464503 + 15776)/2 = 7889.9998732252 (new guess).
Error = new guess - previous value = 15776 - 7889.9998732252 = 7886.0001267748.
7886.0001267748 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 63100 by the previous result. d = 63100/7889.9998732252 = 7.9974652743.
Average this value (d) with that of step 3: (7.9974652743 + 7889.9998732252)/2 = 3948.9986692498 (new guess).
Error = new guess - previous value = 7889.9998732252 - 3948.9986692498 = 3941.0012039754.
3941.0012039754 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 63100 by the previous result. d = 63100/3948.9986692498 = 15.9787341767.
Average this value (d) with that of step 4: (15.9787341767 + 3948.9986692498)/2 = 1982.4887017133 (new guess).
Error = new guess - previous value = 3948.9986692498 - 1982.4887017133 = 1966.5099675365.
1966.5099675365 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 63100 by the previous result. d = 63100/1982.4887017133 = 31.8286807614.
Average this value (d) with that of step 5: (31.8286807614 + 1982.4887017133)/2 = 1007.1586912374 (new guess).
Error = new guess - previous value = 1982.4887017133 - 1007.1586912374 = 975.3300104759.
975.3300104759 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 63100 by the previous result. d = 63100/1007.1586912374 = 62.6514972754.
Average this value (d) with that of step 6: (62.6514972754 + 1007.1586912374)/2 = 534.9050942564 (new guess).
Error = new guess - previous value = 1007.1586912374 - 534.9050942564 = 472.253596981.
472.253596981 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 63100 by the previous result. d = 63100/534.9050942564 = 117.9648514803.
Average this value (d) with that of step 7: (117.9648514803 + 534.9050942564)/2 = 326.4349728684 (new guess).
Error = new guess - previous value = 534.9050942564 - 326.4349728684 = 208.470121388.
208.470121388 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 63100 by the previous result. d = 63100/326.4349728684 = 193.3003668251.
Average this value (d) with that of step 8: (193.3003668251 + 326.4349728684)/2 = 259.8676698468 (new guess).
Error = new guess - previous value = 326.4349728684 - 259.8676698468 = 66.5673030216.
66.5673030216 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 63100 by the previous result. d = 63100/259.8676698468 = 242.8158917852.
Average this value (d) with that of step 9: (242.8158917852 + 259.8676698468)/2 = 251.341780816 (new guess).
Error = new guess - previous value = 259.8676698468 - 251.341780816 = 8.5258890308.
8.5258890308 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 63100 by the previous result. d = 63100/251.341780816 = 251.0525699115.
Average this value (d) with that of step 10: (251.0525699115 + 251.341780816)/2 = 251.1971753638 (new guess).
Error = new guess - previous value = 251.341780816 - 251.1971753638 = 0.1446054522.
0.1446054522 > 0.001. As error > accuracy, we repeat this step again.
Step 12:
Divide 63100 by the previous result. d = 63100/251.1971753638 = 251.1970921194.
Average this value (d) with that of step 11: (251.1970921194 + 251.1971753638)/2 = 251.1971337416 (new guess).
Error = new guess - previous value = 251.1971753638 - 251.1971337416 = 0.0000416222.
0.0000416222 <= 0.001. As error <= accuracy, we stop the iterations and use 251.1971337416 as the square root.
So, we can say that the square root of 63100 is 251.1971
