Question

solve square root 6710

Answer 1

The square root of 6710 is 81.91458966509. Or, 
√6710 = 81.91458966509
............
Step 1: 
 Divide the number (6710) by 2 to get the first guess for the square root .
 First guess = 6710/2 = 3355.Step 2:
 Divide 6710 by the previous result. d = 6710/3355 = 2.
 Average this value (d) with that of step 1: (2 + 3355)/2 = 1678.5 (new guess).
 Error = new guess - previous value = 3355 - 1678.5 = 1676.5.
 1676.5 > 0.001. As error > accuracy, we repeat this step again.Step 3:
 Divide 6710 by the previous result. d = 6710/1678.5 = 3.9976169199.
 Average this value (d) with that of step 2: (3.9976169199 + 1678.5)/2 = 841.24880846(new guess).
 Error = new guess - previous value = 1678.5 - 841.24880846 = 837.25119154.
 837.25119154 > 0.001. As error > accuracy, we repeat this step again.Step 4:
 Divide 6710 by the previous result. d = 6710/841.24880846 = 7.9762371519.
 Average this value (d) with that of step 3: (7.9762371519 + 841.24880846)/2 = 424.612522806 (new guess).
 Error = new guess - previous value = 841.24880846 - 424.612522806 = 416.636285654.
 416.636285654 > 0.001. As error > accuracy, we repeat this step again.Step 5:
 Divide 6710 by the previous result. d = 6710/424.612522806 = 15.802642738.
 Average this value (d) with that of step 4: (15.802642738 + 424.612522806)/2 = 220.207582772 (new guess).
 Error = new guess - previous value = 424.612522806 - 220.207582772 = 204.404940034.
 204.404940034 > 0.001. As error > accuracy, we repeat this step again.Step 6:
 Divide 6710 by the previous result. d = 6710/220.207582772 = 30.4712486079.
 Average this value (d) with that of step 5: (30.4712486079 + 220.207582772)/2 = 125.33941569 (new guess).
 Error = new guess - previous value = 220.207582772 - 125.33941569 = 94.868167082.
 94.868167082 > 0.001. As error > accuracy, we repeat this step again.Step 7:
 Divide 6710 by the previous result. d = 6710/125.33941569 = 53.5346360366.
 Average this value (d) with that of step 6: (53.5346360366 + 125.33941569)/2 = 89.4370258633 (new guess).
 Error = new guess - previous value = 125.33941569 - 89.4370258633 = 35.9023898267.
 35.9023898267 > 0.001. As error > accuracy, we repeat this step again.Step 8:
 Divide 6710 by the previous result. d = 6710/89.4370258633 = 75.0248561514.
 Average this value (d) with that of step 7: (75.0248561514 + 89.4370258633)/2 = 82.2309410074 (new guess).
 Error = new guess - previous value = 89.4370258633 - 82.2309410074 = 7.2060848559.
 7.2060848559 > 0.001. As error > accuracy, we repeat this step again.Step 9:
 Divide 6710 by the previous result. d = 6710/82.2309410074 = 81.5994553607.
 Average this value (d) with that of step 8: (81.5994553607 + 82.2309410074)/2 = 81.9151981841 (new guess).
 Error = new guess - previous value = 82.2309410074 - 81.9151981841 = 0.3157428233.
 0.3157428233 > 0.001. As error > accuracy, we repeat this step again.Step 10:
 Divide 6710 by the previous result. d = 6710/81.9151981841 = 81.9139811506.
 Average this value (d) with that of step 9: (81.9139811506 + 81.9151981841)/2 = 81.9145896674 (new guess).
 Error = new guess - previous value = 81.9151981841 - 81.9145896674 = 0.0006085167.
 0.0006085167 <= 0.001. As error <= accuracy, we stop the iterations and use 81.9145896674 as the square root.

So, we can say that the square root of 6710 is 81.914 with an error smaller than 0.001 (in fact the error is 0.0006085167). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(6710)' is 81.91458966508958.

Note: There are other ways to calculate square roots. This is only one of them.

Answer 2

81.92 the answer on questions √6710