390700 find the square root by long division method
Answers
Answer:
Step 1:
Divide the number (390700) by 2 to get the first guess for the square root .
First guess = 390700/2 = 195350.
Step 2:
Divide 390700 by the previous result. d = 390700/195350 = 2.
Average this value (d) with that of step 1: (2 + 195350)/2 = 97676 (new guess).
Error = new guess - previous value = 195350 - 97676 = 97674.
97674 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 390700 by the previous result. d = 390700/97676 = 3.9999590483.
Average this value (d) with that of step 2: (3.9999590483 + 97676)/2 = 48839.9999795242 (new guess).
Error = new guess - previous value = 97676 - 48839.9999795242 = 48836.0000204758.
48836.0000204758 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 390700 by the previous result. d = 390700/48839.9999795242 = 7.9995905029.
Average this value (d) with that of step 3: (7.9995905029 + 48839.9999795242)/2 = 24423.9997850135 (new guess).
Error = new guess - previous value = 48839.9999795242 - 24423.9997850135 = 24416.0001945107.
24416.0001945107 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 390700 by the previous result. d = 390700/24423.9997850135 = 15.9965609007.
Average this value (d) with that of step 4: (15.9965609007 + 24423.9997850135)/2 = 12219.9981729571 (new guess).
Error = new guess - previous value = 24423.9997850135 - 12219.9981729571 = 12204.0016120564.
12204.0016120564 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 390700 by the previous result. d = 390700/12219.9981729571 = 31.9721815397.
Average this value (d) with that of step 5: (31.9721815397 + 12219.9981729571)/2 = 6125.9851772484 (new guess).
Error = new guess - previous value = 12219.9981729571 - 6125.9851772484 = 6094.0129957087.
6094.0129957087 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 390700 by the previous result. d = 390700/6125.9851772484 = 63.7774967937.
Average this value (d) with that of step 6: (63.7774967937 + 6125.9851772484)/2 = 3094.8813370211 (new guess).
Error = new guess - previous value = 6125.9851772484 - 3094.8813370211 = 3031.1038402273.
3031.1038402273 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 390700 by the previous result. d = 390700/3094.8813370211 = 126.2407043936.
Average this value (d) with that of step 7: (126.2407043936 + 3094.8813370211)/2 = 1610.5610207074 (new guess).
Error = new guess - previous value = 3094.8813370211 - 1610.5610207074 = 1484.3203163137.
1484.3203163137 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 390700 by the previous result. d = 390700/1610.5610207074 = 242.5862758236.
Average this value (d) with that of step 8: (242.5862758236 + 1610.5610207074)/2 = 926.5736482655 (new guess).
Error = new guess - previous value = 1610.5610207074 - 926.5736482655 = 683.9873724419.
683.9873724419 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 390700 by the previous result. d = 390700/926.5736482655 = 421.6610311888.
Average this value (d) with that of step 9: (421.6610311888 + 926.5736482655)/2 = 674.1173397272 (new guess).
Error = new guess - previous value = 926.5736482655 - 674.1173397272 = 252.4563085383.
252.4563085383 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 390700 by the previous result. d = 390700/674.1173397272 = 579.5726900574.
Average this value (d) with that of step 10: (579.5726900574 + 674.1173397272)/2 = 626.8450148923 (new guess).
Error = new guess - previous value = 674.1173397272 - 626.8450148923 = 47.2723248349.
47.2723248349 > 0.001. As error > accuracy, we repeat this step again.
Step 12:
Divide 390700 by the previous result. d = 390700/626.8450148923 = 623.2800624045.
Average this value (d) with that of step 11: (623.2800624045 + 626.8450148923)/2 = 625.0625386484 (new guess).
Error = new guess - previous value = 626.8450148923 - 625.0625386484 = 1.7824762439.
1.7824762439 > 0.001. As error > accuracy, we repeat this step again.
Step 13:
Divide 390700 by the previous result. d = 390700/625.0625386484 = 625.0574556025.
Average this value (d) with that of step 12: (625.0574556025 + 625.0625386484)/2 = 625.0599971255 (new guess).
Error = new guess - previous value = 625.0625386484 - 625.0599971255 = 0.0025415229.
0.0025415229 > 0.001. As error > accuracy, we repeat this step again.
Step 14:
Divide 390700 by the previous result. d = 390700/625.0599971255 = 625.0599971151.
Average this value (d) with that of step 13: (625.0599971151 + 625.0599971255)/2 = 625.0599971203 (new guess).
Error = new guess - previous value = 625.0599971255 - 625.0599971203 = 5.2e-9.
5.2e-9 <= 0.001. As error <= accuracy, we stop the iterations and use 625.0599971203 as the square root.
So, we can say that the square root of 390700 is -19.18509728 with an error smaller than 0.001 (in fact the error is 5.2e-9).