5712 square root by long division method beith all steps
Answers
Answer:
Step 1:
Divide the number (5712) by 2 to get the first guess for the square root .
First guess = 5712/2 = 2856.
Step 2:
Divide 5712 by the previous result. d = 5712/2856 = 2.
Average this value (d) with that of step 1: (2 + 2856)/2 = 1429 (new guess).
Error = new guess - previous value = 2856 - 1429 = 1427.
1427 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 5712 by the previous result. d = 5712/1429 = 3.9972008397.
Average this value (d) with that of step 2: (3.9972008397 + 1429)/2 = 716.4986004199 (new guess).
Error = new guess - previous value = 1429 - 716.4986004199 = 712.5013995801.
712.5013995801 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 5712 by the previous result. d = 5712/716.4986004199 = 7.9721021041.
Average this value (d) with that of step 3: (7.9721021041 + 716.4986004199)/2 = 362.235351262 (new guess).
Error = new guess - previous value = 716.4986004199 - 362.235351262 = 354.2632491579.
354.2632491579 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 5712 by the previous result. d = 5712/362.235351262 = 15.768753602.
Average this value (d) with that of step 4: (15.768753602 + 362.235351262)/2 = 189.002052432 (new guess).
Error = new guess - previous value = 362.235351262 - 189.002052432 = 173.23329883.
173.23329883 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 5712 by the previous result. d = 5712/189.002052432 = 30.2218940297.
Average this value (d) with that of step 5: (30.2218940297 + 189.002052432)/2 = 109.6119732309 (new guess).
Error = new guess - previous value = 189.002052432 - 109.6119732309 = 79.3900792011.
79.3900792011 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 5712 by the previous result. d = 5712/109.6119732309 = 52.1110954546.
Average this value (d) with that of step 6: (52.1110954546 + 109.6119732309)/2 = 80.8615343428 (new guess).
Error = new guess - previous value = 109.6119732309 - 80.8615343428 = 28.7504388881.
28.7504388881 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 5712 by the previous result. d = 5712/80.8615343428 = 70.6392730045.
Average this value (d) with that of step 7: (70.6392730045 + 80.8615343428)/2 = 75.7504036737 (new guess).
Error = new guess - previous value = 80.8615343428 - 75.7504036737 = 5.1111306691.
5.1111306691 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 5712 by the previous result. d = 5712/75.7504036737 = 75.405538756.
Average this value (d) with that of step 8: (75.405538756 + 75.7504036737)/2 = 75.5779712149 (new guess).
Error = new guess - previous value = 75.7504036737 - 75.5779712149 = 0.1724324588.
0.1724324588 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 5712 by the previous result. d = 5712/75.5779712149 = 75.5775778071.
Average this value (d) with that of step 9: (75.5775778071 + 75.5779712149)/2 = 75.577774511 (new guess).
Error = new guess - previous value = 75.5779712149 - 75.577774511 = 0.0001967039.
0.0001967039 <= 0.001. As error <= accuracy, we stop the iterations and use 75.577774511 as the square root.
So, we can say that the square root of 5712 is 75.577 with an error smaller than 0.001 (in fact the error is 0.0001967039). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(5712)' is 75.57777451076474.
Note: There are other ways to calculate square roots. This is only one of them.