Question

how to find square root of 10.4

Answer 1

Step 1: 
 Divide the number (10.4) by 2 to get the first guess for the square root .
 First guess = 10.4/2 = 5.2.Step 2:
 Divide 10.4 by the previous result. d = 10.4/5.2 = 2.
 Average this value (d) with that of step 1: (2 + 5.2)/2 = 3.6 (new guess).
 Error = new guess - previous value = 5.2 - 3.6 = 1.6.
 1.6 > 0.001. As error > accuracy, we repeat this step again.Step 3:
 Divide 10.4 by the previous result. d = 10.4/3.6 = 2.8888888889.
 Average this value (d) with that of step 2: (2.8888888889 + 3.6)/2 = 3.2444444445(new guess).
 Error = new guess - previous value = 3.6 - 3.2444444445 = 0.3555555555.
 0.3555555555 > 0.001. As error > accuracy, we repeat this step again.Step 4:
 Divide 10.4 by the previous result. d = 10.4/3.2444444445 = 3.205479452.
 Average this value (d) with that of step 3: (3.205479452 + 3.2444444445)/2 =3.2249619483 (new guess).
 Error = new guess - previous value = 3.2444444445 - 3.2249619483 = 0.0194824962.
 0.0194824962 > 0.001. As error > accuracy, we repeat this step again.Step 5:
 Divide 10.4 by the previous result. d = 10.4/3.2249619483 = 3.2248442514.
 Average this value (d) with that of step 4: (3.2248442514 + 3.2249619483)/2 =3.2249030998 (new guess).
 Error = new guess - previous value = 3.2249619483 - 3.2249030998 = 0.0000588485.
 0.0000588485 <= 0.001. As error <= accuracy, we stop the iterations and use 3.2249030998 as the square root.

So, we can say that the square root of 10.4 is 3.2249 with an error smaller than 0.001 (in fact the error is 0.0000588485). this means that the first 4 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(10.4)' is 3.22490309931942.

Answer 2

Answer:

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