find the square root of 9809 by long division method.
Answers
Step 1:
Divide the number (9809) by 2 to get the first guess for the square root .
First guess = 9809/2 = 4904.5.
Step 2:
Divide 9809 by the previous result. d = 9809/4904.5 = 2.
Average this value (d) with that of step 1: (2 + 4904.5)/2 = 2453.25 (new guess).
Error = new guess - previous value = 4904.5 - 2453.25 = 2451.25.
2451.25 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 9809 by the previous result. d = 9809/2453.25 = 3.9983695098.
Average this value (d) with that of step 2: (3.9983695098 + 2453.25)/2 = 1228.6241847549 (new guess).
Error = new guess - previous value = 2453.25 - 1228.6241847549 = 1224.6258152451.
1224.6258152451 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 9809 by the previous result. d = 9809/1228.6241847549 = 7.9837269376.
Average this value (d) with that of step 3: (7.9837269376 + 1228.6241847549)/2 = 618.3039558463 (new guess).
Error = new guess - previous value = 1228.6241847549 - 618.3039558463 = 610.3202289086.
610.3202289086 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 9809 by the previous result. d = 9809/618.3039558463 = 15.8643655879.
Average this value (d) with that of step 4: (15.8643655879 + 618.3039558463)/2 = 317.0841607171 (new guess).
Error = new guess - previous value = 618.3039558463 - 317.0841607171 = 301.2197951292.
301.2197951292 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 9809 by the previous result. d = 9809/317.0841607171 = 30.9350046934.
Average this value (d) with that of step 5: (30.9350046934 + 317.0841607171)/2 = 174.0095827053 (new guess).
Error = new guess - previous value = 317.0841607171 - 174.0095827053 = 143.0745780118.
143.0745780118 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 9809 by the previous result. d = 9809/174.0095827053 = 56.370458727.
Average this value (d) with that of step 6: (56.370458727 + 174.0095827053)/2 = 115.1900207162 (new guess).
Error = new guess - previous value = 174.0095827053 - 115.1900207162 = 58.8195619891.
58.8195619891 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 9809 by the previous result. d = 9809/115.1900207162 = 85.1549460536.
Average this value (d) with that of step 7: (85.1549460536 + 115.1900207162)/2 = 100.1724833849 (new guess).
Error = new guess - previous value = 115.1900207162 - 100.1724833849 = 15.0175373313.
15.0175373313 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 9809 by the previous result. d = 9809/100.1724833849 = 97.9211023681.
Average this value (d) with that of step 8: (97.9211023681 + 100.1724833849)/2 = 99.0467928765 (new guess).
Error = new guess - previous value = 100.1724833849 - 99.0467928765 = 1.1256905084.
1.1256905084 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 9809 by the previous result. d = 9809/99.0467928765 = 99.0339991344.
Average this value (d) with that of step 9: (99.0339991344 + 99.0467928765)/2 = 99.0403960055 (new guess).
Error = new guess - previous value = 99.0467928765 - 99.0403960055 = 0.006396871.
0.006396871 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 9809 by the previous result. d = 9809/99.0403960055 = 99.0403955923.
Average this value (d) with that of step 10: (99.0403955923 + 99.0403960055)/2 = 99.0403957989 (new guess).
Error = new guess - previous value = 99.0403960055 - 99.0403957989 = 2.066e-7.
2.066e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 99.0403957989 as the square root.