square root of 8.5 using the division method
Answers
Answer:
The square root of 8.5 is 2.9154759474227. Or,
√8.5 = 2.9154759474227
Answer:
Step 1:
Divide the number (8.5) by 2 to get the first guess for the square root .
First guess = 8.5/2 = 4.25.
Step 2:
Divide 8.5 by the previous result. d = 8.5/4.25 = 2.
Average this value (d) with that of step 1: (2 + 4.25)/2 = 3.125
Error = new guess - previous value = 4.25 - 3.125 = 1.125.
1.125 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 8.5 by the previous result. d = 8.5/3.125 = 2.72.
Average this value (d) with that of step 2: (2.72 + 3.125)/2 = 2.9225
Error = new guess - previous value = 3.125 - 2.9225 = 0.2025.
0.2025 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 8.5 by the previous result. d = 8.5/2.9225 = 2.9084687767.
Average this value (d) with that of step 3: (2.9084687767 + 2.9225)/2 = 2.9154843884
Error = new guess - previous value = 2.9225 - 2.9154843884 = 0.0070156116.
0.0070156116 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 8.5 by the previous result. d = 8.5/2.9154843884 = 2.9154675065.
Average this value (d) with that of step 4: (2.9154675065 + 2.9154843884)/2 = 2.9154759475
Error = new guess - previous value = 2.9154843884 - 2.9154759475 = 0.0000084409.
0.0000084409 <= 0.001. As error <= accuracy, we stop the iterations and use 2.9154759475 as the square root.
So, we can say that the square root of 8.5 is 2.91547 with an error smaller than 0.001 (in fact the error is 0.0000084409). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(8.5)' is 2.9154759474226504.
Step-by-step explanation:
Hope it will help