4900 find root by division method
Answers
Step-by-step explanation:
Step 1:
Divide the number (4900) by 2 to get the first guess for the square root .
First guess = 4900/2 = 2450.
Step 2:
Divide 4900 by the previous result. d = 4900/2450 = 2.
Average this value (d) with that of step 1: (2 + 2450)/2 = 1226 (new guess).
Error = new guess - previous value = 2450 - 1226 = 1224.
1224 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 4900 by the previous result. d = 4900/1226 = 3.9967373573.
Average this value (d) with that of step 2: (3.9967373573 + 1226)/2 = 614.9983686787 (new guess).
Error = new guess - previous value = 1226 - 614.9983686787 = 611.0016313213.
611.0016313213 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 4900 by the previous result. d = 4900/614.9983686787 = 7.967500809.
Average this value (d) with that of step 3: (7.967500809 + 614.9983686787)/2 = 311.4829347438 (new guess).
Error = new guess - previous value = 614.9983686787 - 311.4829347438 = 303.5154339349.
303.5154339349 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 4900 by the previous result. d = 4900/311.4829347438 = 15.7311988987.
Average this value (d) with that of step 4: (15.7311988987 + 311.4829347438)/2 = 163.6070668212 (new guess).
Error = new guess - previous value = 311.4829347438 - 163.6070668212 = 147.8758679226.
147.8758679226 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 4900 by the previous result. d = 4900/163.6070668212 = 29.9498065408.
Average this value (d) with that of step 5: (29.9498065408 + 163.6070668212)/2 = 96.778436681 (new guess).
Error = new guess - previous value = 163.6070668212 - 96.778436681 = 66.8286301402.
66.8286301402 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 4900 by the previous result. d = 4900/96.778436681 = 50.6311133765.
Average this value (d) with that of step 6: (50.6311133765 + 96.778436681)/2 = 73.7047750287 (new guess).
Error = new guess - previous value = 96.778436681 - 73.7047750287 = 23.0736616523.
23.0736616523 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 4900 by the previous result. d = 4900/73.7047750287 = 66.4814457149.
Average this value (d) with that of step 7: (66.4814457149 + 73.7047750287)/2 = 70.0931103718 (new guess).
Error = new guess - previous value = 73.7047750287 - 70.0931103718 = 3.6116646569.
3.6116646569 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 4900 by the previous result. d = 4900/70.0931103718 = 69.9070133143.
Average this value (d) with that of step 8: (69.9070133143 + 70.0931103718)/2 = 70.000061843 (new guess).
Error = new guess - previous value = 70.0931103718 - 70.000061843 = 0.0930485288.
0.0930485288 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 4900 by the previous result. d = 4900/70.000061843 = 69.9999381571.
Average this value (d) with that of step 9: (69.9999381571 + 70.000061843)/2 = 70 (new guess).
Error = new guess - previous value = 70.000061843 - 70 = 0.000061843.
0.000061843 <= 0.001. As error <= accuracy, we stop the iterations and use 70 as the square root.
So, we can say that the square root of 4900 is 70
Step 1:
Divide the number (4900) by 2 to get the first guess for the square root .
First guess = 4900/2 = 2450.
Step 2:
Divide 4900 by the previous result. d = 4900/2450 = 2.
Average this value (d) with that of step 1: (2 + 2450)/2 = 1226 (new guess).
Error = new guess - previous value = 2450 - 1226 = 1224.
1224 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 4900 by the previous result. d = 4900/1226 = 3.9967373573.
Average this value (d) with that of step 2: (3.9967373573 + 1226)/2 = 614.9983686787 (new guess).
Error = new guess - previous value = 1226 - 614.9983686787 = 611.0016313213.
611.0016313213 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 4900 by the previous result. d = 4900/614.9983686787 = 7.967500809.
Average this value (d) with that of step 3: (7.967500809 + 614.9983686787)/2 = 311.4829347438 (new guess).
Error = new guess - previous value = 614.9983686787 - 311.4829347438 = 303.5154339349.
303.5154339349 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 4900 by the previous result. d = 4900/311.4829347438 = 15.7311988987.
Average this value (d) with that of step 4: (15.7311988987 + 311.4829347438)/2 = 163.6070668212 (new guess).
Error = new guess - previous value = 311.4829347438 - 163.6070668212 = 147.8758679226.
147.8758679226 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 4900 by the previous result. d = 4900/163.6070668212 = 29.9498065408.
Average this value (d) with that of step 5: (29.9498065408 + 163.6070668212)/2 = 96.778436681 (new guess).
Error = new guess - previous value = 163.6070668212 - 96.778436681 = 66.8286301402.
66.8286301402 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 4900 by the previous result. d = 4900/96.778436681 = 50.6311133765.
Average this value (d) with that of step 6: (50.6311133765 + 96.778436681)/2 = 73.7047750287 (new guess).
Error = new guess - previous value = 96.778436681 - 73.7047750287 = 23.0736616523.
23.0736616523 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 4900 by the previous result. d = 4900/73.7047750287 = 66.4814457149.
Average this value (d) with that of step 7: (66.4814457149 + 73.7047750287)/2 = 70.0931103718 (new guess).
Error = new guess - previous value = 73.7047750287 - 70.0931103718 = 3.6116646569.
3.6116646569 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 4900 by the previous result. d = 4900/70.0931103718 = 69.9070133143.
Average this value (d) with that of step 8: (69.9070133143 + 70.0931103718)/2 = 70.000061843 (new guess).
Error = new guess - previous value = 70.0931103718 - 70.000061843 = 0.0930485288.
0.0930485288 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 4900 by the previous result. d = 4900/70.000061843 = 69.9999381571.
Average this value (d) with that of step 9: (69.9999381571 + 70.000061843)/2 = 70 (new guess).
Error = new guess - previous value = 70.000061843 - 70 = 0.000061843.
0.000061843 <= 0.001. As error <= accuracy, we stop the iterations and use 70 as the square root.
So, we can say that the square root of 4900 is 70 with an error smaller than 0.001 (in fact the error is 0.000061843). this means that the first 4 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(4900)' is 70.