.Find the square root of 40.96
pls explain with steps
Answers
Step 1:
Divide the number (40.96) by 2 to get the first guess for the square root .
First guess = 40.96/2 = 20.48
Step 2:
Divide 40.96 by the previous result. d = 40.96/20.48 = 2.
Average this value (d) with that of step 1: (2 + 20.48)/2 = 11.24 (new guess).
Error = new guess - previous value = 20.48 - 11.24 = 9.24.
9.24 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 40.96 by the previous result. d = 40.96/11.24 = 3.6441281139.
Average this value (d) with that of step 2: (3.6441281139 + 11.24)/2 = 7.442064057 (new guess).
Error = new guess - previous value = 11.24 - 7.442064057 = 3.797935943.
3.797935943 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 40.96 by the previous result. d = 40.96/7.442064057 = 5.5038494276.
Average this value (d) with that of step 3: (5.5038494276 + 7.442064057)/2 = 6.4729567423 (new guess).
Error = new guess - previous value = 7.442064057 - 6.4729567423 = 0.9691073147.
0.9691073147 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 40.96 by the previous result. d = 40.96/6.4729567423 = 6.3278655537.
Average this value (d) with that of step 4: (6.3278655537 + 6.4729567423)/2 = 6.400411148 (new guess).
Error = new guess - previous value = 6.4729567423 - 6.400411148 = 0.0725455943.
0.0725455943 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 40.96 by the previous result. d = 40.96/6.400411148 = 6.3995888784.
Average this value (d) with that of step 5: (6.3995888784 + 6.400411148)/2 = 6.4000000132 (new guess).
Error = new guess - previous value = 6.400411148 - 6.4000000132 = 0.0004111348.
0.0004111348 <= 0.001. As error <= accuracy, we stop the iterations and use 6.4000000132 as the square root.