Question

evaluate √7056 from long division method

Answer 1

kaksysiekjxkalxjksllwjsjskaoa

Answer 2

HEYA MATE,

HERE IS UR ANSWER.

Thanks for asking this question.

Step 1:
Divide the number (7056) by 2 to get the first guess for the square root .
First guess = 7056/2 = 3528.

Step 2:
Divide 7056 by the previous result. d = 7056/3528 = 2.
Average this value (d) with that of step 1: (2 + 3528)/2 = 1765 (new guess).
Error = new guess - previous value = 3528 - 1765 = 1763.
1763 > 0.001. As error > accuracy, we repeat this step again.

Step 3:
Divide 7056 by the previous result. d = 7056/1765 = 3.997733711.
Average this value (d) with that of step 2: (3.997733711 + 1765)/2 = 884.4988668555 (new guess).
Error = new guess - previous value = 1765 - 884.4988668555 = 880.5011331445.
880.5011331445 > 0.001. As error > accuracy, we repeat this step again.

Step 4:
Divide 7056 by the previous result. d = 7056/884.4988668555 = 7.977398575.
Average this value (d) with that of step 3: (7.977398575 + 884.4988668555)/2 = 446.2381327153 (new guess).
Error = new guess - previous value = 884.4988668555 - 446.2381327153 = 438.2607341402.
438.2607341402 > 0.001. As error > accuracy, we repeat this step again.

Step 5:
Divide 7056 by the previous result. d = 7056/446.2381327153 = 15.8121852049.
Average this value (d) with that of step 4: (15.8121852049 + 446.2381327153)/2 = 231.0251589601 (new guess).
Error = new guess - previous value = 446.2381327153 - 231.0251589601 = 215.2129737552.
215.2129737552 > 0.001. As error > accuracy, we repeat this step again.

Step 6:
Divide 7056 by the previous result. d = 7056/231.0251589601 = 30.5421281031.
Average this value (d) with that of step 5: (30.5421281031 + 231.0251589601)/2 = 130.7836435316 (new guess).
Error = new guess - previous value = 231.0251589601 - 130.7836435316 = 100.2415154285.
100.2415154285 > 0.001. As error > accuracy, we repeat this step again.

Step 7:
Divide 7056 by the previous result. d = 7056/130.7836435316 = 53.9517007591.
Average this value (d) with that of step 6: (53.9517007591 + 130.7836435316)/2 = 92.3676721454 (new guess).
Error = new guess - previous value = 130.7836435316 - 92.3676721454 = 38.4159713862.
38.4159713862 > 0.001. As error > accuracy, we repeat this step again.

Step 8:
Divide 7056 by the previous result. d = 7056/92.3676721454 = 76.3903629496.
Average this value (d) with that of step 7: (76.3903629496 + 92.3676721454)/2 = 84.3790175475 (new guess).
Error = new guess - previous value = 92.3676721454 - 84.3790175475 = 7.9886545979.
7.9886545979 > 0.001. As error > accuracy, we repeat this step again.

Step 9:
Divide 7056 by the previous result. d = 7056/84.3790175475 = 83.6226849409.
Average this value (d) with that of step 8: (83.6226849409 + 84.3790175475)/2 = 84.0008512442 (new guess).
Error = new guess - previous value = 84.3790175475 - 84.0008512442 = 0.3781663033.
0.3781663033 > 0.001. As error > accuracy, we repeat this step again.

Step 10:
Divide 7056 by the previous result. d = 7056/84.0008512442 = 83.9991487644.
Average this value (d) with that of step 9: (83.9991487644 + 84.0008512442)/2 = 84.0000000043 (new guess).
Error = new guess - previous value = 84.0008512442 - 84.0000000043 = 0.0008512399.
0.0008512399 <= 0.001. As error <= accuracy, we stop the iterations and use 84.0000000043 as the square root.
So, we can say that the square root of 7056 is 84 with an error smaller than 0.001 (in fact the error is 0.0008512399). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(7056)' is 84.

I HOPE IT HELPS U.