find the square root by long division method 3625
Answers
Answer:
Step 1:
Divide the number (3625) by 2 to get the first guess for the square root .
First guess = 3625/2 = 1812.5.
Step 2:
Divide 3625 by the previous result. d = 3625/1812.5 = 2.
Average this value (d) with that of step 1: (2 + 1812.5)/2 = 907.25 (new guess).
Error = new guess - previous value = 1812.5 - 907.25 = 905.25.
905.25 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 3625 by the previous result. d = 3625/907.25 = 3.9955910719.
Average this value (d) with that of step 2: (3.9955910719 + 907.25)/2 = 455.622795536 (new guess).
Error = new guess - previous value = 907.25 - 455.622795536 = 451.627204464.
451.627204464 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 3625 by the previous result. d = 3625/455.622795536 = 7.9561427468.
Average this value (d) with that of step 3: (7.9561427468 + 455.622795536)/2 = 231.7894691414 (new guess).
Error = new guess - previous value = 455.622795536 - 231.7894691414 = 223.8333263946.
223.8333263946 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 3625 by the previous result. d = 3625/231.7894691414 = 15.6391919505.
Average this value (d) with that of step 4: (15.6391919505 + 231.7894691414)/2 = 123.714330546 (new guess).
Error = new guess - previous value = 231.7894691414 - 123.714330546 = 108.0751385954.
108.0751385954 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 3625 by the previous result. d = 3625/123.714330546 = 29.301375063.
Average this value (d) with that of step 5: (29.301375063 + 123.714330546)/2 = 76.5078528045 (new guess).
Error = new guess - previous value = 123.714330546 - 76.5078528045 = 47.2064777415.
47.2064777415 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 3625 by the previous result. d = 3625/76.5078528045 = 47.3807572311.
Average this value (d) with that of step 6: (47.3807572311 + 76.5078528045)/2 = 61.9443050178 (new guess).
Error = new guess - previous value = 76.5078528045 - 61.9443050178 = 14.5635477867.
14.5635477867 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 3625 by the previous result. d = 3625/61.9443050178 = 58.5203110917.
Average this value (d) with that of step 7: (58.5203110917 + 61.9443050178)/2 = 60.2323080548 (new guess).
Error = new guess - previous value = 61.9443050178 - 60.2323080548 = 1.711996963.
1.711996963 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 3625 by the previous result. d = 3625/60.2323080548 = 60.1836475651.
Average this value (d) with that of step 8: (60.1836475651 + 60.2323080548)/2 = 60.20797781 (new guess).
Error = new guess - previous value = 60.2323080548 - 60.20797781 = 0.0243302448.
0.0243302448 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 3625 by the previous result. d = 3625/60.20797781 = 60.2079679779.
Average this value (d) with that of step 9: (60.2079679779 + 60.20797781)/2 = 60.207972894 (new guess).
Error = new guess - previous value = 60.20797781 - 60.207972894 = 0.000004916.
0.000004916 <= 0.001. As error <= accuracy, we stop the iterations and use 60.207972894 as the square root.
So, we can say that the square root of 3625 is 60.20797 with an error smaller than 0.001 (in fact the error is 0.000004916). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(3625)' is 60.207972893961475.
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what is the square root of 3625