using division method find the Square root 6586
Answers
Answer:
Step 1:
Divide the number (6586) by 2 to get the first guess for the square root .
First guess = 6586/2 = 3293.
Step 2:
Divide 6586 by the previous result. d = 6586/3293 = 2.
Average this value (d) with that of step 1: (2 + 3293)/2 = 1647.5 (new guess).
Error = new guess - previous value = 3293 - 1647.5 = 1645.5.
1645.5 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 6586 by the previous result. d = 6586/1647.5 = 3.9975720789.
Average this value (d) with that of step 2: (3.9975720789 + 1647.5)/2 = 825.7487860395 (new guess).
Error = new guess - previous value = 1647.5 - 825.7487860395 = 821.7512139605.
821.7512139605 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 6586 by the previous result. d = 6586/825.7487860395 = 7.9757913198.
Average this value (d) with that of step 3: (7.9757913198 + 825.7487860395)/2 = 416.8622886797 (new guess).
Error = new guess - previous value = 825.7487860395 - 416.8622886797 = 408.8864973598.
408.8864973598 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 6586 by the previous result. d = 6586/416.8622886797 = 15.798982491.
Average this value (d) with that of step 4: (15.798982491 + 416.8622886797)/2 = 216.3306355854 (new guess).
Error = new guess - previous value = 416.8622886797 - 216.3306355854 = 200.5316530943.
200.5316530943 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 6586 by the previous result. d = 6586/216.3306355854 = 30.4441392786.
Average this value (d) with that of step 5: (30.4441392786 + 216.3306355854)/2 = 123.387387432 (new guess).
Error = new guess - previous value = 216.3306355854 - 123.387387432 = 92.9432481534.
92.9432481534 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 6586 by the previous result. d = 6586/123.387387432 = 53.3766062891.
Average this value (d) with that of step 6: (53.3766062891 + 123.387387432)/2 = 88.3819968606 (new guess).
Error = new guess - previous value = 123.387387432 - 88.3819968606 = 35.0053905714.
35.0053905714 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 6586 by the previous result. d = 6586/88.3819968606 = 74.5174383239.
Average this value (d) with that of step 7: (74.5174383239 + 88.3819968606)/2 = 81.4497175923 (new guess).
Error = new guess - previous value = 88.3819968606 - 81.4497175923 = 6.9322792683.
6.9322792683 > 0.001. As error > accuracy, we repeat this step again.
Step 9:
Divide 6586 by the previous result. d = 6586/81.4497175923 = 80.8597033199.
Average this value (d) with that of step 8: (80.8597033199 + 81.4497175923)/2 = 81.1547104561 (new guess).
Error = new guess - previous value = 81.4497175923 - 81.1547104561 = 0.2950071362.
0.2950071362 > 0.001. As error > accuracy, we repeat this step again.
Step 10:
Divide 6586 by the previous result. d = 6586/81.1547104561 = 81.1536380696.
Average this value (d) with that of step 9: (81.1536380696 + 81.1547104561)/2 = 81.1541742629 (new guess).
Error = new guess - previous value = 81.1547104561 - 81.1541742629 = 0.0005361932.
0.0005361932 <= 0.001. As error <= accuracy, we stop the iterations and use 81.1541742629 as the square root.
So, we can say that the square root of 6586 is 81.154 with an error smaller than 0.001 (in fact the error is 0.0005361932). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(6586)' is 81.15417426109393.