please give me solution of root of 0.6 step by step
Answers
Answer:
Now I have given the answer in steps....
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 (0.6) by 2 to get the first guess for the square root .
First guess = 0.6/2 = 0.3.
Step 2:
Divide 0.6 by the previous result. d = 0.6/0.3 = 2.
Average this value (d) with that of step 1: (2 + 0.3)/2 = 1.15 (new guess).
Error = new guess - previous value = 0.3 - 1.15 = 0.85.
0.85 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 0.6 by the previous result. d = 0.6/1.15 = 0.5217391304.
Average this value (d) with that of step 2: (0.5217391304 + 1.15)/2 = 0.8358695652 (new guess).
Error = new guess - previous value = 1.15 - 0.8358695652 = 0.3141304348.
0.3141304348 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 0.6 by the previous result. d = 0.6/0.8358695652 = 0.7178153446.
Average this value (d) with that of step 3: (0.7178153446 + 0.8358695652)/2 = 0.7768424549 (new guess).
Error = new guess - previous value = 0.8358695652 - 0.7768424549 = 0.0590271103.
0.0590271103 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 0.6 by the previous result. d = 0.6/0.7768424549 = 0.772357376.
Average this value (d) with that of step 4: (0.772357376 + 0.7768424549)/2 = 0.7745999155 (new guess).
Error = new guess - previous value = 0.7768424549 - 0.7745999155 = 0.0022425394.
0.0022425394 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 0.6 by the previous result. d = 0.6/0.7745999155 = 0.774593423.
Average this value (d) with that of step 5: (0.774593423 + 0.7745999155)/2 = 0.7745966692 (new guess).
Error = new guess - previous value = 0.7745999155 - 0.7745966692 = 0.0000032463.
0.0000032463 <= 0.001. As error <= accuracy, we stop the iterations and use 0.7745966692 as the square root.
So, we can say that the square root of 0.6 is 0.77459 with an error smaller than 0.001 (in fact the error is 0.0000032463). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(0.6)' is 0.7745966692414834.
Note: There are other ways to calculate square roots. This is only one of them.
Answer:
0.7745966692414834 is the answer... hope thil will help you