find the square root of 8832 by long division method
Answers
Answer:
Divide the number (8832) by 2 to get the first guess for the square root .
First guess = 8832/2 = 4416.
Step 2:
Divide 8832 by the previous result. d = 8832/4416 = 2.
Average this value (d) with that of step 1: (2 + 4416)/2 = 2209 (new guess).
Error = new guess - previous value = 4416 - 2209 = 2207.
2207 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 8832 by the previous result. d = 8832/2209 = 3.9981892259.
Average this value (d) with that of step 2: (3.9981892259 + 2209)/2 = 1106.499094613 (new guess).
Error = new guess - previous value = 2209 - 1106.499094613 = 1102.500905387.
1102.500905387 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 8832 by the previous result. d = 8832/1106.499094613 = 7.9819315199.
Average this value (d) with that of step 3: (7.9819315199 + 1106.499094613)/2 = 557.2405130664 (new guess).
Error = new guess - previous value = 1106.499094613 - 557.2405130664 = 549.2585815466.
549.2585815466 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 8832 by the previous result. d = 8832/557.2405130664 = 15.8495295889.
Average this value (d) with that of step 4: (15.8495295889 + 557.2405130664)/2 = 286.5450213277 (new guess).
Error = new guess - previous value = 557.2405130664 - 286.5450213277 = 270.6954917387.
270.6954917387 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 8832 by the previous result. d = 8832/286.5450213277 = 30.8223816246.
Average this value (d) with that of step 5: (30.8223816246 + 286.5450213277)/2 = 158.6837014762 (new guess).
Error = new guess - previous value = 286.5450213277 - 158.6837014762 = 127.8613198515.
127.8613198515 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 8832 by the previous result. d = 8832/158.6837014762 = 55.6578899902.
Average this value (d) with that of step 6: (55.6578899902 + 158.6837014762)/2 = 107.1707957332 (new guess).
Error = new guess - previous value = 158.6837014762 - 107.1707957332 = 51.512905743.
51.512905743 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 8832 by the previous result. d = 8832/107.1707957332 = 82.4105106207.
Average this value (d) with that of step 7: (82.4105106207 + 107.1707957332)/2 = 94.790653177 (new guess).
Error = new guess - previous value = 107.1707957332 - 94.790653177 = 12.3801425562.
12.3801425562 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 8832 by the previous result. d = 8832/94.790653177 = 93.173743444.
Average this value (d) with that of step 8: (93.173743444 + 94.790653177)/2 = 93.9821983105 (new guess).
Error = new guess - previous value = 94.790653177 - 93.9821983105 = 0.8084548665.
0.8084548665 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 8832 by the previous result. d = 8832/93.9821983105 = 93.9752438097.
Average this value (d) with that of step 9: (93.9752438097 + 93.9821983105)/2 = 93.9787210601 (new guess).
Error = new guess - previous value = 93.9821983105 - 93.9787210601 = 0.0034772504.
0.0034772504 > 0.001. As error > accuracy, we repeat this step again.
Step 11:
Divide 8832 by the previous result. d = 8832/93.9787210601 = 93.9787209314.
Average this value (d) with that of step 10: (93.9787209314 + 93.9787210601)/2 = 93.9787209958 (new guess).
Error = new guess - previous value = 93.9787210601 - 93.9787209958 = 6.43e-8.
6.43e-8 <= 0.001. As error <= accuracy, we stop the iterations and use 93.9787209958 as the square root.
So, we can say that the square root of 8832 is 93.9787209 with an error smaller than 0.001 (in fact the error is 6.43e-8). this means that the first 7 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(8832)' is 93.97872099576584.(hope it's helps u)