√0.1 =? (a)0.1 (b)0.01 (c)0.316 (d)none of these Please tell me step by step
Answers
Step-by-step explanation:
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There is several method from which you can find squre root..
In this case we are going to use the 'Babylonian Method' to get the square root of any positive number.
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 (0.1) by 2 to get the first guess for the square root .
First guess = 0.1/2 = 0.05.
Step 2:
Divide 0.1 by the previous result. d = 0.1/0.05 = 2.
Average this value (d) with that of step 1: (2 + 0.05)/2 = 1.025 (new guess).
Error = new guess - previous value = 0.05 - 1.025 = 0.975.
0.975 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 0.1 by the previous result. d = 0.1/1.025 = 0.0975609756.
Average this value (d) with that of step 2: (0.0975609756 + 1.025)/2 = 0.5612804878 (new guess).
Error = new guess - previous value = 1.025 - 0.5612804878 = 0.4637195122.
0.4637195122 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 0.1 by the previous result. d = 0.1/0.5612804878 = 0.1781640413.
Average this value (d) with that of step 3: (0.1781640413 + 0.5612804878)/2 = 0.3697222645 (new guess).
Error = new guess - previous value = 0.5612804878 - 0.3697222645 = 0.1915582233.
0.1915582233 > 0.001. As error > accuracy, we repeat this step again.
Step 5:
Divide 0.1 by the previous result. d = 0.1/0.3697222645 = 0.2704732974.
Average this value (d) with that of step 4: (0.2704732974 + 0.3697222645)/2 = 0.3200977809 (new guess).
Error = new guess - previous value = 0.3697222645 - 0.3200977809 = 0.0496244836.
0.0496244836 > 0.001. As error > accuracy, we repeat this step again.
Step 6:
Divide 0.1 by the previous result. d = 0.1/0.3200977809 = 0.31240454.
Average this value (d) with that of step 5: (0.31240454 + 0.3200977809)/2 = 0.3162511605 (new guess).
Error = new guess - previous value = 0.3200977809 - 0.3162511605 = 0.0038466204.
0.0038466204 > 0.001. As error > accuracy, we repeat this step again.
Step 7:
Divide 0.1 by the previous result. d = 0.1/0.3162511605 = 0.3162043733.
Average this value (d) with that of step 6: (0.3162043733 + 0.3162511605)/2 = 0.3162277669 (new guess).
Error = new guess - previous value = 0.3162511605 - 0.3162277669 = 0.0000233936.
0.0000233936 <= 0.001. As error <= accuracy, we stop the iterations and use 0.3162277669 as the square root.
2) you can also try calculator..:-)