Answer:

Step 1:

Divide the number (7250) by 2 to get the FIRST guess for the square root .

First guess = 7250/2 = 3625.

Step 2:

Divide 7250 by the previous result. d = 7250/3625 = 2.

Average this value (d) with that of step 1: (2 + 3625)/2 = 1813.5 (new guess).

Error = new guess - previous value = 3625 - 1813.5 = 1811.5.

1811.5 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 7250 by the previous result. d = 7250/1813.5 = 3.9977943204.

Average this value (d) with that of step 2: (3.9977943204 + 1813.5)/2 = 908.7488971602 (new guess).

Error = new guess - previous value = 1813.5 - 908.7488971602 = 904.7511028398.

904.7511028398 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 7250 by the previous result. d = 7250/908.7488971602 = 7.9780014288.

Average this value (d) with that of step 3: (7.9780014288 + 908.7488971602)/2 = 458.3634492945 (new guess).

Error = new guess - previous value = 908.7488971602 - 458.3634492945 = 450.3854478657.

450.3854478657 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 7250 by the previous result. d = 7250/458.3634492945 = 15.8171425125.

Average this value (d) with that of step 4: (15.8171425125 + 458.3634492945)/2 = 237.0902959035 (new guess).

Error = new guess - previous value = 458.3634492945 - 237.0902959035 = 221.273153391.

221.273153391 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 7250 by the previous result. d = 7250/237.0902959035 = 30.5790668166.

Average this value (d) with that of step 5: (30.5790668166 + 237.0902959035)/2 = 133.83468136 (new guess).

Error = new guess - previous value = 237.0902959035 - 133.83468136 = 103.2556145435.

103.2556145435 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

Divide 7250 by the previous result. d = 7250/133.83468136 = 54.1713099051.

Average this value (d) with that of step 6: (54.1713099051 + 133.83468136)/2 = 94.0029956326 (new guess).

Error = new guess - previous value = 133.83468136 - 94.0029956326 = 39.8316857274.

39.8316857274 > 0.001. As error > accuracy, we repeat this step again.

Step 8:

Divide 7250 by the previous result. d = 7250/94.0029956326 = 77.1252017152.

Average this value (d) with that of step 7: (77.1252017152 + 94.0029956326)/2 = 85.5640986739 (new guess).

Error = new guess - previous value = 94.0029956326 - 85.5640986739 = 8.4388969587.

8.4388969587 > 0.001. As error > accuracy, we repeat this step again.

Step 9:

Divide 7250 by the previous result. d = 7250/85.5640986739 = 84.7317988778.

Average this value (d) with that of step 8: (84.7317988778 + 85.5640986739)/2 = 85.1479487759 (new guess).

Error = new guess - previous value = 85.5640986739 - 85.1479487759 = 0.416149898.

0.416149898 > 0.001. As error > accuracy, we repeat this step again.

Step 10:

Divide 7250 by the previous result. d = 7250/85.1479487759 = 85.1459148955.

Average this value (d) with that of step 9: (85.1459148955 + 85.1479487759)/2 = 85.1469318357 (new guess).

Error = new guess - previous value = 85.1479487759 - 85.1469318357 = 0.0010169402.

0.0010169402 > 0.001. As error > accuracy, we repeat this step again.

Step 11:

Divide 7250 by the previous result. d = 7250/85.1469318357 = 85.1469318236.

Average this value (d) with that of step 10: (85.1469318236 + 85.1469318357)/2 = 85.1469318297 (new guess).

Error = new guess - previous value = 85.1469318357 - 85.1469318297 = 6e-9.

6e-9 <= 0.001. As error <= accuracy, we STOP the iterations and USE 85.1469318297 as the square root.

So, we can say that the square root of 7250 is -0.7524141 with an error smaller than 0.001 (in fact the error is 6e-9). this means that the first 8 decimal places are CORRECT. Just to compare, the returned value by using the javascript function 'Math.sqrt(7250)' is 85.14693182963201.

Note: There are other ways to calculate square roots. This is only one of them.