Question

find the square of 99.8 using formula....​

Answer 1

Answer:

Divide 99.8 by the previous result. d = 99.8/49.9 = 2. Average this value (d) with that of step 1: (2 + 49.9)/2 = 25.95 (new guess).

Answer 2

Step 1:

Divide the number (99.8) by 2 to get the first guess for the square root .

First guess = 99.8/2 = 49.9.

Step 2:

Divide 99.8 by the previous result. d = 99.8/49.9 = 2.

Average this value (d) with that of step 1: (2 + 49.9)/2 = 25.95 (new guess).

Error = new guess - previous value = 49.9 - 25.95 = 23.95.

23.95 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 99.8 by the previous result. d = 99.8/25.95 = 3.8458574181.

Average this value (d) with that of step 2: (3.8458574181 + 25.95)/2 = 14.8979287091 (new guess).

Error = new guess - previous value = 25.95 - 14.8979287091 = 11.0520712909.

11.0520712909 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 99.8 by the previous result. d = 99.8/14.8979287091 = 6.6989178126.

Average this value (d) with that of step 3: (6.6989178126 + 14.8979287091)/2 = 10.7984232609 (new guess).

Error = new guess - previous value = 14.8979287091 - 10.7984232609 = 4.0995054482.

4.0995054482 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 99.8 by the previous result. d = 99.8/10.7984232609 = 9.2420900338.

Average this value (d) with that of step 4: (9.2420900338 + 10.7984232609)/2 = 10.0202566473 (new guess).

Error = new guess - previous value = 10.7984232609 - 10.0202566473 = 0.7781666136.

0.7781666136 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 99.8 by the previous result. d = 99.8/10.0202566473 = 9.9598247343.

Average this value (d) with that of step 5: (9.9598247343 + 10.0202566473)/2 = 9.9900406908 (new guess).

Error = new guess - previous value = 10.0202566473 - 9.9900406908 = 0.0302159565.

0.0302159565 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

Divide 99.8 by the previous result. d = 99.8/9.9900406908 = 9.9899492994.

Average this value (d) with that of step 6: (9.9899492994 + 9.9900406908)/2 = 9.9899949951 (new guess).

Error = new guess - previous value = 9.9900406908 - 9.9899949951 = 0.0000456957.

0.0000456957 <= 0.001. As error <= accuracy, we stop the iterations and use 9.9899949951 as the square root.

So, we can say that the square root of 99.8 is 9.9899 with an error smaller than 0.001 (in fact the error is 0.0000456957). this means that the first 4 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(99.8)' is 9.989994994993742.