find the square root of 753.5025 by long division method
Answers
Answer:
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Step-by-step explanation:
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Answer:
•Step 1:
Divide the number (753.5025) by 2 to get the first guess for the square root.
First guess = 753.5025/2 = 376.75125.
•Step 2:
Divide 753.5025 by the previous result. d = 753.5025/376.75125 = 2.
Average this value (d) with that of step 1: (2 + 376.75125)/2 = 189.375625 (new guess).
Error = new guess - previous value = 376.75125 - 189.375625 = 187.375625.
187.375625 > 0.001. As error > accuracy, we repeat this step again.
•Step 3:
Divide 753.5025 by the previous result. d = 753.5025/189.375625 = 3.9788779575.
Average this value (d) with that of step 2: (3.9788779575 + 189.375625)/2 = 96.6772514788 (new guess).
Error = new guess - previous value = 189.375625 - 96.6772514788 = 92.6983735212.
92.6983735212 > 0.001. As error > accuracy, we repeat this step again.
•Step 4:
Divide 753.5025 by the previous result. d = 753.5025/96.6772514788 = 7.7940000204.
Average this value (d) with that of step 3: (7.7940000204 + 96.6772514788)/2 = 52.2356257496 (new guess).
Error = new guess - previous value = 96.6772514788 - 52.2356257496 = 44.4416257292.
44.4416257292 > 0.001. As error > accuracy, we repeat this step again.
•Step 5:
Divide 753.5025 by the previous result. d = 753.5025/52.2356257496 = 14.425068891.
Average this value (d) with that of step 4: (14.425068891 + 52.2356257496)/2 = 33.3303473203 (new guess).
Error = new guess - previous value = 52.2356257496 - 33.3303473203 = 18.9052784293.
18.9052784293 > 0.001. As error > accuracy, we repeat this step again.
•Step 6:
Divide 753.5025 by the previous result. d = 753.5025/33.3303473203 = 22.6071001529.
Average this value (d) with that of step 5: (22.6071001529 + 33.3303473203)/2 = 27.9687237366 (new guess).
Error = new guess - previous value = 33.3303473203 - 27.9687237366 = 5.3616235837.
5.3616235837 > 0.001. As error > accuracy, we repeat this step again.
•Step 7:
Divide 753.5025 by the previous result. d = 753.5025/27.9687237366 = 26.9408968066.
Average this value (d) with that of step 6: (26.9408968066 + 27.9687237366)/2 = 27.4548102716 (new guess).
Error = new guess - previous value = 27.9687237366 - 27.4548102716 = 0.513913465.
0.513913465 > 0.001. As error > accuracy, we repeat this step again.
•Step 8:
Divide 753.5025 by the previous result. d = 753.5025/27.4548102716 = 27.4451905712.
Average this value (d) with that of step 7: (27.4451905712 + 27.4548102716)/2 = 27.4500004214 (new guess).
Error = new guess - previous value = 27.4548102716 - 27.4500004214 = 0.0048098502.
0.0048098502 > 0.001. As error > accuracy, we repeat this step again.
•Step 9:
Divide 753.5025 by the previous result. d = 753.5025/27.4500004214 = 27.4499995786.
Average this value (d) with that of step 8: (27.4499995786 + 27.4500004214)/2 = 27.45 (new guess).
Error = new guess - previous value = 27.4500004214 - 27.45 = 4.214e-7.
4.214e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 27.45 as the square root.
=>So, we can say that the square root of 753.5025 is 27.45 with an error smaller than 0.001 (in fact the error is 4.214e-7). this means that the first 6 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(753.5025)' is 27.45.
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