Question

square root of 80.41 by long division method
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Answer 1

Answer:

The square root of 80.41 is 8.9671623159169. Or,

√80.41 = 8.9671623159169

See, below on this web page, details on how to calculate this square root using the Babylonian Method

Answer 2

Answer:

The square root of 80.41 is 8.9671623159169. Or,

√80.41 = 8.9671623159169

Step-by-step explanation:

Step 1:

 Divide the number (80.41) by 2 to get the first guess for the square root .

 First guess = 80.41/2 = 40.205.

Step 2:

 Divide 80.41 by the previous result. d = 80.41/40.205 = 2.

 Average this value (d) with that of step 1: (2 + 40.205)/2 = 21.1025 (new guess).

 Error = new guess - previous value = 40.205 - 21.1025 = 19.1025.

 19.1025 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

 Divide 80.41 by the previous result. d = 80.41/21.1025 = 3.8104489989.

 Average this value (d) with that of step 2: (3.8104489989 + 21.1025)/2 = 12.4564744995 (new guess).

 Error = new guess - previous value = 21.1025 - 12.4564744995 = 8.6460255005.

 8.6460255005 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

 Divide 80.41 by the previous result. d = 80.41/12.4564744995 = 6.4552775348.

 Average this value (d) with that of step 3: (6.4552775348 + 12.4564744995)/2 = 9.4558760172 (new guess).

 Error = new guess - previous value = 12.4564744995 - 9.4558760172 = 3.0005984823.

 3.0005984823 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

 Divide 80.41 by the previous result. d = 80.41/9.4558760172 = 8.5037070974.

 Average this value (d) with that of step 4: (8.5037070974 + 9.4558760172)/2 = 8.9797915573 (new guess).

 Error = new guess - previous value = 9.4558760172 - 8.9797915573 = 0.4760844599.

 0.4760844599 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

 Divide 80.41 by the previous result. d = 80.41/8.9797915573 = 8.9545508364.

 Average this value (d) with that of step 5: (8.9545508364 + 8.9797915573)/2 = 8.9671711969 (new guess).

 Error = new guess - previous value = 8.9797915573 - 8.9671711969 = 0.0126203604.

 0.0126203604 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

 Divide 80.41 by the previous result. d = 80.41/8.9671711969 = 8.9671534349.

 Average this value (d) with that of step 6: (8.9671534349 + 8.9671711969)/2 = 8.9671623159 (new guess).

 Error = new guess - previous value = 8.9671711969 - 8.9671623159 = 0.000008881.

 0.000008881 <= 0.001. As error <= accuracy, we stop the iterations and use 8.9671623159 as the square root.