Question

find the square root of 760384 step by step n also find the value of √76.0384-√0.760384​

Answer 1

Answer:

Step 1:

Divide the number (0.04) by 2 to get the first guess for the square root .

First guess = 0.04/2 = 0.02. (Note if you could guess a better value, the process could be shorter).

Step 2:

Divide 0.04 by the previous result. d = 0.04/0.02 = 2.

Average this value (d) with that of step 1: (2 + 0.02)/2 = 1.01 (new guess).

Error = new guess - previous value = 0.02 - 1.01 = 0.99.

0.99 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 0.04 by the previous result. d = 0.04/1.01 = 0.039604.

Average this value (d) with that of step 2: (0.039604 + 1.01)/2 = 0.524802 (new guess).

Error = new guess - previous value = 1.01 - 0.524802 = 0.485198.

0.485198 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 0.04 by the previous result. d = 0.04/0.524802 = 0.076219.

Average this value (d) with that of step 3: (0.076219 + 0.524802)/2 = 0.300511 (new guess).

Error = new guess - previous value = 0.524802 - 0.300511 = 0.224291.

0.224291 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 0.04 by the previous result. d = 0.04/0.300511 = 0.133107.

Average this value (d) with that of step 4: (0.133107 + 0.300511)/2 = 0.216809 (new guess).

Error = new guess - previous value = 0.300511 - 0.216809 = 0.083702.

0.083702 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 0.04 by the previous result. d = 0.04/0.216809 = 0.184494.

Average this value (d) with that of step 5: (0.184494 + 0.216809)/2 = 0.200651 (new guess).

Error = new guess - previous value = 0.216809 - 0.200651 = 0.016158.

0.016158 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

Divide 0.04 by the previous result. d = 0.04/0.200651 = 0.199351.

Average this value (d) with that of step 6: (0.199351 + 0.200651)/2 = 0.200001 (new guess).

Error = new guess - previous value = 0.200651 - 0.200001 = 0.00065.

0.00065 <= 0.001. As error <= accuracy, we stop the iterations and use 0.200001 as the square root.

So, we can say that the square root of 0.04 is 0.200001 with an error smaller than 0.001 (in fact the error is 0.00065). this means that first 3 decimal places are correct.

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