find the square root of 3259 by division method
Answers
Answer:
Step 1:
Divide the number (3259) by 2 to get the first guess for the square root .
First guess = 3259/2 = 1629.5.
Step 2:
Divide 3259 by the previous result. d = 3259/1629.5 = 2.
Average this value (d) with that of step 1: (2 + 1629.5)/2 = 815.75 (new guess).
Error = new guess - previous value = 1629.5 - 815.75 = 813.75.
813.75 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 3259 by the previous result. d = 3259/815.75 = 3.9950965369.
Average this value (d) with that of step 2: (3.9950965369 + 815.75)/2 = 409.8725482684 (new guess).
Error = new guess - previous value = 815.75 - 409.8725482684 = 405.8774517316.
405.8774517316 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 3259 by the previous result. d = 3259/409.8725482684 = 7.9512521972.
Average this value (d) with that of step 3: (7.9512521972 + 409.8725482684)/2 = 208.9119002328 (new guess).
Error = new guess - previous value = 409.8725482684 - 208.9119002328 = 200.9606480356.
200.9606480356 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 3259 by the previous result. d = 3259/208.9119002328 = 15.5998772515.
Average this value (d) with that of step 4: (15.5998772515 + 208.9119002328)/2 = 112.2558887422 (new guess).
Error = new guess - previous value = 208.9119002328 - 112.2558887422 = 96.6560114906.
96.6560114906 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 3259 by the previous result. d = 3259/112.2558887422 = 29.031884532.
Average this value (d) with that of step 5: (29.031884532 + 112.2558887422)/2 = 70.6438866371 (new guess).
Error = new guess - previous value = 112.2558887422 - 70.6438866371 = 41.6120021051.
41.6120021051 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 3259 by the previous result. d = 3259/70.6438866371 = 46.132795846.
Average this value (d) with that of step 6: (46.132795846 + 70.6438866371)/2 = 58.3883412416 (new guess).
Error = new guess - previous value = 70.6438866371 - 58.3883412416 = 12.2555453955.
12.2555453955 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 3259 by the previous result. d = 3259/58.3883412416 = 55.8159374063.
Average this value (d) with that of step 7: (55.8159374063 + 58.3883412416)/2 = 57.102139324 (new guess).
Error = new guess - previous value = 58.3883412416 - 57.102139324 = 1.2862019176.
1.2862019176 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 3259 by the previous result. d = 3259/57.102139324 = 57.0731681611.
Average this value (d) with that of step 8: (57.0731681611 + 57.102139324)/2 = 57.0876537426 (new guess).
Error = new guess - previous value = 57.102139324 - 57.0876537426 = 0.0144855814.
0.0144855814 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 3259 by the previous result. d = 3259/57.0876537426 = 57.0876500669.
Average this value (d) with that of step 9: (57.0876500669 + 57.0876537426)/2 = 57.0876519048 (new guess).
Error = new guess - previous value = 57.0876537426 - 57.0876519048 = 0.0000018378.
0.0000018378 <= 0.001. As error <= accuracy, we stop the iterations and use 57.0876519048 as the square root.
So, we can say that the square root of 3259 is 57.08765 with an error smaller than 0.001 (in fact the error is 0.0000018378). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(3259)' is 57.087651904768336.
Answer:
square root of 3259 is;
Step-by-step explanation:57.08765190476834