squre root 9.216 decimal place
Answers
Answer:
Step-by-step explanation:
We must set an error for the final result. Say, smaller than 0.001. In other words we will try to find the square root value with at least 2 correct decimal places.
Step 1:
Divide the number (92.16) by 2 to get the first guess for the square root .
First guess = 92.16/2 = 46.08.
Step 2:
Divide 92.16 by the previous result. d = 92.16/46.08 = 2.
Average this value (d) with that of step 1: (2 + 46.08)/2 = 24.04 (new guess).
Error = new guess - previous value = 46.08 - 24.04 = 22.04.
22.04 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 92.16 by the previous result. d = 92.16/24.04 = 3.8336106489.
Average this value (d) with that of step 2: (3.8336106489 + 24.04)/2 = 13.9368053245 (new guess).
Error = new guess - previous value = 24.04 - 13.9368053245 = 10.1031946755.
10.1031946755 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 92.16 by the previous result. d = 92.16/13.9368053245 = 6.6127062734.
Average this value (d) with that of step 3: (6.6127062734 + 13.9368053245)/2 = 10.274755799 (new guess).
Error = new guess - previous value = 13.9368053245 - 10.274755799 = 3.6620495255.
3.6620495255 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 92.16 by the previous result. d = 92.16/10.274755799 = 8.9695562408.
Average this value (d) with that of step 4: (8.9695562408 + 10.274755799)/2 = 9.6221560199 (new guess).
Error = new guess - previous value = 10.274755799 - 9.6221560199 = 0.6525997791.
0.6525997791 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 92.16 by the previous result. d = 92.16/9.6221560199 = 9.5778949967.
Average this value (d) with that of step 5: (9.5778949967 + 9.6221560199)/2 = 9.6000255083 (new guess).
Error = new guess - previous value = 9.6221560199 - 9.6000255083 = 0.0221305116.
0.0221305116 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 92.16 by the previous result. d = 92.16/9.6000255083 = 9.5999744918.
Average this value (d) with that of step 6: (9.5999744918 + 9.6000255083)/2 = 9.6 (new guess).
Error = new guess - previous value = 9.6000255083 - 9.6 = 0.0000255083.
0.0000255083 <= 0.001. As error <= accuracy, we stop the iterations and use 9.6 as the square root.
So, we can say that the square root of 92.16 is 9.6 with an error smaller than 0.001 (in fact the error is 0.0000255083). this means that the first 4 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(92.16)' is 9.6.
Note: There are other ways to calculate square roots. This is only one of them.
Answer:
muche thanks jarur de
Step-by-step explanation:
96 = underroot 9216
root 92.16 = 9.6
=> 9.6 + 9.216 = 18.816
hope ie helps