find the square root of 59.29 explain step by step plz
Answers
Explanation:
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Explanation:
Step 1:
Divide the number (59.29) by 2 to get the first guess for the square root .
First guess = 59.29/2 = 29.645.
Step 2:
Divide 59.29 by the previous result. d = 59.29/29.645 = 2.
Average this value (d) with that of step 1: (2 + 29.645)/2 = 15.8225 (new guess).
Error = new guess - previous value = 29.645 - 15.8225 = 13.8225.
13.8225 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 59.29 by the previous result. d = 59.29/15.8225 = 3.7471954495.
Average this value (d) with that of step 2: (3.7471954495 + 15.8225)/2 = 9.7848477248 (new guess).
Error = new guess - previous value = 15.8225 - 9.7848477248 = 6.0376522752.
6.0376522752 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 59.29 by the previous result. d = 59.29/9.7848477248 = 6.0593686961.
Average this value (d) with that of step 3: (6.0593686961 + 9.7848477248)/2 = 7.9221082105 (new guess).
Error = new guess - previous value = 9.7848477248 - 7.9221082105 = 1.8627395143.
1.8627395143 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 59.29 by the previous result. d = 59.29/7.9221082105 = 7.484118927.
Average this value (d) with that of step 4: (7.484118927 + 7.9221082105)/2 = 7.7031135688 (new guess).
Error = new guess - previous value = 7.9221082105 - 7.7031135688 = 0.2189946417.
0.2189946417 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 59.29 by the previous result. d = 59.29/7.7031135688 = 7.6968876897.
Average this value (d) with that of step 5: (7.6968876897 + 7.7031135688)/2 = 7.7000006293 (new guess).
Error = new guess - previous value = 7.7031135688 - 7.7000006293 = 0.0031129395.
0.0031129395 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 59.29 by the previous result. d = 59.29/7.7000006293 = 7.6999993707.
Average this value (d) with that of step 6: (7.6999993707 + 7.7000006293)/2 = 7.7 (new guess).
Error = new guess - previous value = 7.7000006293 - 7.7 = 6.293e-7.
6.293e-7 <= 0.001. As error <= accuracy, we stop the iterations and use 7.7 as the square root