Square root of 206116 step by step
Answers
Answer:
Step 1:
Divide the number (206116) by 2 = 206116/2 = 103058.
Step 2:
Divide 206116 by the previous result. d = 206116/103058 = 2.
Average this value (d) with that of step 1: (2 + 103058)/2 = 51530 (new guess).
Error = new guess - previous value = 103058 - 51530 = 51528.
51528 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 206116 by the previous result. d = 206116/51530 = 3.9999223753.
Average this value (d) with that of step 2: (3.9999223753 + 51530)/2 = 25766.9999611876 (new guess).
Error = new guess - previous value = 51530 - 25766.9999611876 = 25763.0000388124.
25763.0000388124 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 206116 by the previous result. d = 206116/25766.9999611876 = 7.9992238255.
Average this value (d) with that of step 3: (7.9992238255 + 25766.9999611876)/2 = 12887.4995925066 (new guess).
Error = new guess - previous value = 25766.9999611876 - 12887.4995925066 = 12879.500368681.
12879.500368681 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 206116 by the previous result. d = 206116/12887.4995925066 = 15.993482562.
Average this value (d) with that of step 4: (15.993482562 + 12887.4995925066)/2 = 6451.7465375343 (new guess).
Error = new guess - previous value = 12887.4995925066 - 6451.7465375343 = 6435.7530549723.
6435.7530549723 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 206116 by the previous result. d = 206116/6451.7465375343 = 31.947318265.
Average this value (d) with that of step 5: (31.947318265 + 6451.7465375343)/2 = 3241.8469278997 (new guess).
Error = new guess - previous value = 6451.7465375343 - 3241.8469278997 = 3209.8996096346.
3209.8996096346 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 206116 by the previous result. d = 206116/3241.8469278997 = 63.5798063833.
Average this value (d) with that of step 6: (63.5798063833 + 3241.8469278997)/2 = 1652.7133671415 (new guess).
Error = new guess - previous value = 3241.8469278997 - 1652.7133671415 = 1589.1335607582.
1589.1335607582 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 206116 by the previous result. d = 206116/1652.7133671415 = 124.7137005714.
Average this value (d) with that of step 7: (124.7137005714 + 1652.7133671415)/2 = 888.7135338565 (new guess).
Error = new guess - previous value = 1652.7133671415 - 888.7135338565 = 763.999833285.
763.999833285 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 206116 by the previous result. d = 206116/888.7135338565 = 231.9262531151.
Average this value (d) with that of step 8: (231.9262531151 + 888.7135338565)/2 = 560.3198934858 (new guess).
Error = new guess - previous value = 888.7135338565 - 560.3198934858 = 328.3936403707.
328.3936403707 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 206116 by the previous result. d = 206116/560.3198934858 = 367.8541533083.
Average this value (d) with that of step 9: (367.8541533083 + 560.3198934858)/2 = 464.0870233971 (new guess).
Error = new guess - previous value = 560.3198934858 - 464.0870233971 = 96.2328700887.
96.2328700887 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 206116 by the previous result. d = 206116/464.0870233971 = 444.1322200548.
Average this value (d) with that of step 10: (444.1322200548 + 464.0870233971)/2 = 454.109621726 (new guess).
Error = new guess - previous value = 464.0870233971 - 454.109621726 = 9.9774016711.
9.9774016711 > 0.001. As error > accuracy, we repeat this step again.
Step 12:
Divide 206116 by the previous result. d = 206116/454.109621726 = 453.8904047366.
Average this value (d) with that of step 11: (453.8904047366 + 454.109621726)/2 = 454.0000132313 (new guess).
Error = new guess - previous value = 454.109621726 - 454.0000132313 = 0.1096084947.
0.1096084947 > 0.001. As error > accuracy, we repeat this step again.
Step 13:
Divide 206116 by the previous result. d = 206116/454.0000132313 = 453.9999867687.
Average this value (d) with that of step 12: (453.9999867687 + 454.0000132313)/2 = 454 (new guess).
Error = new guess - previous value = 454.0000132313 - 454 = 0.0000132313.
0.0000132313 <= 0.001. As error <= accuracy, we stop the iterations and use 454 as the square root.