i changed my answer sorry i was wrong the last time :(
Step 1:
Divide the number (530) by 2 to get the first guess for the square root .
First guess = 530/2 = 265.
Step 2:
Divide 530 by the previous result. d = 530/265 = 2.
Average this value (d) with that of step 1: (2 + 265)/2 = 133.5 (new guess).
Error = new guess - previous value = 265 - 133.5 = 131.5.
131.5 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 530 by the previous result. d = 530/133.5 = 3.9700374532.
Average this value (d) with that of step 2: (3.9700374532 + 133.5)/2 = 68.7350187266 (new guess).
Error = new guess - previous value = 133.5 - 68.7350187266 = 64.7649812734.
64.7649812734 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 530 by the previous result. d = 530/68.7350187266 = 7.7107711588.
Average this value (d) with that of step 3: (7.7107711588 + 68.7350187266)/2 = 38.2228949427 (new guess).
Error = new guess - previous value = 68.7350187266 - 38.2228949427 = 30.5121237839.
30.5121237839 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 530 by the previous result. d = 530/38.2228949427 = 13.8660350242.
Average this value (d) with that of step 4: (13.8660350242 + 38.2228949427)/2 = 26.0444649835 (new guess).
Error = new guess - previous value = 38.2228949427 - 26.0444649835 = 12.1784299592.
12.1784299592 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 530 by the previous result. d = 530/26.0444649835 = 20.3498133034.
Average this value (d) with that of step 5: (20.3498133034 + 26.0444649835)/2 = 23.1971391435 (new guess).
Error = new guess - previous value = 26.0444649835 - 23.1971391435 = 2.84732584.
2.84732584 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 530 by the previous result. d = 530/23.1971391435 = 22.8476449928.
Average this value (d) with that of step 6: (22.8476449928 + 23.1971391435)/2 = 23.0223920681 (new guess).
Error = new guess - previous value = 23.1971391435 - 23.0223920681 = 0.1747470754.
0.1747470754 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 530 by the previous result. d = 530/23.0223920681 = 23.0210656839.
Average this value (d) with that of step 7: (23.0210656839 + 23.0223920681)/2 = 23.021728876 (new guess).
Error = new guess - previous value = 23.0223920681 - 23.021728876 = 0.0006631921.
0.0006631921 <= 0.001. As error <= accuracy, we stop the iterations and use 23.021728876 as the square root.
So, we can say that the square root of 530 is 23.021 with an error smaller than 0.001 (in fact the error is 0.0006631921). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(530)' is 23.021728866442675.
Answers & Comments
23.021728866443 ( with solution↓ )
i changed my answer sorry i was wrong the last time :(
Step 1:
Divide the number (530) by 2 to get the first guess for the square root .
First guess = 530/2 = 265.
Step 2:
Divide 530 by the previous result. d = 530/265 = 2.
Average this value (d) with that of step 1: (2 + 265)/2 = 133.5 (new guess).
Error = new guess - previous value = 265 - 133.5 = 131.5.
131.5 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 530 by the previous result. d = 530/133.5 = 3.9700374532.
Average this value (d) with that of step 2: (3.9700374532 + 133.5)/2 = 68.7350187266 (new guess).
Error = new guess - previous value = 133.5 - 68.7350187266 = 64.7649812734.
64.7649812734 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 530 by the previous result. d = 530/68.7350187266 = 7.7107711588.
Average this value (d) with that of step 3: (7.7107711588 + 68.7350187266)/2 = 38.2228949427 (new guess).
Error = new guess - previous value = 68.7350187266 - 38.2228949427 = 30.5121237839.
30.5121237839 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 530 by the previous result. d = 530/38.2228949427 = 13.8660350242.
Average this value (d) with that of step 4: (13.8660350242 + 38.2228949427)/2 = 26.0444649835 (new guess).
Error = new guess - previous value = 38.2228949427 - 26.0444649835 = 12.1784299592.
12.1784299592 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 530 by the previous result. d = 530/26.0444649835 = 20.3498133034.
Average this value (d) with that of step 5: (20.3498133034 + 26.0444649835)/2 = 23.1971391435 (new guess).
Error = new guess - previous value = 26.0444649835 - 23.1971391435 = 2.84732584.
2.84732584 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 530 by the previous result. d = 530/23.1971391435 = 22.8476449928.
Average this value (d) with that of step 6: (22.8476449928 + 23.1971391435)/2 = 23.0223920681 (new guess).
Error = new guess - previous value = 23.1971391435 - 23.0223920681 = 0.1747470754.
0.1747470754 > 0.001. As error > accuracy, we repeat this step again.
Step 8:
Divide 530 by the previous result. d = 530/23.0223920681 = 23.0210656839.
Average this value (d) with that of step 7: (23.0210656839 + 23.0223920681)/2 = 23.021728876 (new guess).
Error = new guess - previous value = 23.0223920681 - 23.021728876 = 0.0006631921.
0.0006631921 <= 0.001. As error <= accuracy, we stop the iterations and use 23.021728876 as the square root.
So, we can say that the square root of 530 is 23.021 with an error smaller than 0.001 (in fact the error is 0.0006631921). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(530)' is 23.021728866442675.
Answer:
23.0217288664
Step-by-step explanation:
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