the square root of 346.7 in long division
Answers
Answer:
Do you know that I don't know the answer of this question
search in google for the answer
Step-by-step explanation:
Step 1:
Divide the number (346.7) by 2 to get the first guess for the square root .
First guess = 346.7/2 = 173.35.
Step 2:
Divide 346.7 by the previous result. d = 346.7/173.35 = 2.
Average this value (d) with that of step 1: (2 + 173.35)/2 = 87.675 (new guess).
Error = new guess - previous value = 173.35 - 87.675 = 85.675.
85.675 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 346.7 by the previous result. d = 346.7/87.675 = 3.9543769604.
Average this value (d) with that of step 2: (3.9543769604 + 87.675)/2 = 45.8146884802 (new guess).
Error = new guess - previous value = 87.675 - 45.8146884802 = 41.8603115198.
41.8603115198 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 346.7 by the previous result. d = 346.7/45.8146884802 = 7.5674420475.
Average this value (d) with that of step 3: (7.5674420475 + 45.8146884802)/2 = 26.6910652639 (new guess).
Error = new guess - previous value = 45.8146884802 - 26.6910652639 = 19.1236232163.
19.1236232163 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 346.7 by the previous result. d = 346.7/26.6910652639 = 12.9893654139.
Average this value (d) with that of step 4: (12.9893654139 + 26.6910652639)/2 = 19.8402153389 (new guess).
Error = new guess - previous value = 26.6910652639 - 19.8402153389 = 6.850849925.
6.850849925 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 346.7 by the previous result. d = 346.7/19.8402153389 = 17.4746087216.
Average this value (d) with that of step 5: (17.4746087216 + 19.8402153389)/2 = 18.6574120303 (new guess).
Error = new guess - previous value = 19.8402153389 - 18.6574120303 = 1.1828033086.
1.1828033086 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 346.7 by the previous result. d = 346.7/18.6574120303 = 18.5824271575.
Average this value (d) with that of step 6: (18.5824271575 + 18.6574120303)/2 = 18.6199195939 (new guess).
Error = new guess - previous value = 18.6574120303 - 18.6199195939 = 0.0374924364.
0.0374924364 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 346.7 by the previous result. d = 346.7/18.6199195939 = 18.6198441004.
Average this value (d) with that of step 7: (18.6198441004 + 18.6199195939)/2 = 18.6198818472 (new guess).
Error = new guess - previous value = 18.6199195939 - 18.6198818472 = 0.0000377467.
0.0000377467 <= 0.001. As error <= accuracy, we stop the iterations and use 18.6198818472 as the square root.
So, we can say that the square root of 346.7 is 18.6198 with an error smaller than 0.001 (in fact the error is 0.0000377467). this means that the first 4 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(346.7)' is 18.619881847100963.
Note: There are other ways to calculate square roots. This is only one of them.