Find the square root of 5.76 by division method.
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Answers
Answer:
answer is given in the attachment
Answer:
2.4 answer
Step 1:
Divide the number (5.76) by 2 to get the first guess for the square root .
First guess = 5.76/2 = 2.88.
Step 2:
Divide 5.76 by the previous result. d = 5.76/2.88 = 2.
Average this value (d) with that of step 1: (2 + 2.88)/2 = 2.44 (new guess).
Error = new guess - previous value = 2.88 - 2.44 = 0.44.
0.44 > 0.001. As error > accuracy, we repeat this step again.
Step 3:
Divide 5.76 by the previous result. d = 5.76/2.44 = 2.3606557377.
Average this value (d) with that of step 2: (2.3606557377 + 2.44)/2 = 2.4003278689 (new guess).
Error = new guess - previous value = 2.44 - 2.4003278689 = 0.0396721311.
0.0396721311 > 0.001. As error > accuracy, we repeat this step again.
Step 4:
Divide 5.76 by the previous result. d = 5.76/2.4003278689 = 2.3996721759.
Average this value (d) with that of step 3: (2.3996721759 + 2.4003278689)/2 = 2.4000000224 (new guess).
Error = new guess - previous value = 2.4003278689 - 2.4000000224 = 0.0003278465.
0.0003278465 <= 0.001. As error <= accuracy, we stop the iterations and use 2.4000000224 as the square root.
So, we can say that the square root of 5.76 is 2.4 with an error smaller than 0.001 (in fact the error is 0.0003278465). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(5.76)' is 2.4.
Note: There are other ways to calculate square roots. This is only one of them.