Question

find the square root of 248​

Answer 1

Answer:

15.748

Step-by-step explanation:

Step 1:

Divide the number (248) by 2 to get the first guess for the square root .

First guess = 248/2 = 124.

Step 2:

Divide 248 by the previous result. d = 248/124 = 2.

Average this value (d) with that of step 1: (2 + 124)/2 = 63 (new guess).

Error = new guess - previous value = 124 - 63 = 61.

61 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 248 by the previous result. d = 248/63 = 3.936508.

Average this value (d) with that of step 2: (3.936508 + 63)/2 = 33.468254 (new guess).

Error = new guess - previous value = 63 - 33.468254 = 29.531746.

29.531746 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 248 by the previous result. d = 248/33.468254 = 7.410007.

Average this value (d) with that of step 3: (7.410007 + 33.468254)/2 = 20.439131 (new guess).

Error = new guess - previous value = 33.468254 - 20.439131 = 13.029123.

13.029123 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 248 by the previous result. d = 248/20.439131 = 12.133588.

Average this value (d) with that of step 4: (12.133588 + 20.439131)/2 = 16.28636 (new guess).

Error = new guess - previous value = 20.439131 - 16.28636 = 4.152771.

4.152771 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 248 by the previous result. d = 248/16.28636 = 15.227466.

Average this value (d) with that of step 5: (15.227466 + 16.28636)/2 = 15.756913 (new guess).

Error = new guess - previous value = 16.28636 - 15.756913 = 0.529447.

0.529447 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

Divide 248 by the previous result. d = 248/15.756913 = 15.739124.

Average this value (d) with that of step 6: (15.739124 + 15.756913)/2 = 15.748019 (new guess).

Error = new guess - previous value = 15.756913 - 15.748019 = 0.008894.

0.008894 > 0.001. As error > accuracy, we repeat this step again.

Step 8:

Divide 248 by the previous result. d = 248/15.748019 = 15.748012.

Average this value (d) with that of step 7: (15.748012 + 15.748019)/2 = 15.748016 (new guess).

Error = new guess - previous value = 15.748019 - 15.748016 = 0.000003.

0.000003 <= 0.001. As error <= accuracy, we stop the iterations and use 15.748016 as the square root.