Question

Question 18: Square root of
123.6 correct up to 2 decimal
place is ? *​

Answer 1

√123.6 correct upto 2 decimal points is 11.11

Answer 2

Step-by-step explanation:

Step 1:

Divide the number (123.6) by 2 to get the first guess for the square root .

First guess = 123.6/2 = 61.8.

Step 2:

Divide 123.6 by the previous result. d = 123.6/61.8 = 2.

Average this value (d) with that of step 1: (2 + 61.8)/2 = 31.9 (new guess).

Error = new guess - previous value = 61.8 - 31.9 = 29.9.

29.9 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 123.6 by the previous result. d = 123.6/31.9 = 3.8746081505.

Average this value (d) with that of step 2: (3.8746081505 + 31.9)/2 = 17.8873040753 (new guess).

Error = new guess - previous value = 31.9 - 17.8873040753 = 14.0126959247.

14.0126959247 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 123.6 by the previous result. d = 123.6/17.8873040753 = 6.9099289351.

Average this value (d) with that of step 3: (6.9099289351 + 17.8873040753)/2 = 12.3986165052 (new guess).

Error = new guess - previous value = 17.8873040753 - 12.3986165052 = 5.4886875701.

5.4886875701 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 123.6 by the previous result. d = 123.6/12.3986165052 = 9.9688541821.

Average this value (d) with that of step 4: (9.9688541821 + 12.3986165052)/2 = 11.1837353437 (new guess).

Error = new guess - previous value = 12.3986165052 - 11.1837353437 = 1.2148811615.

1.2148811615 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 123.6 by the previous result. d = 123.6/11.1837353437 = 11.051763673.

Average this value (d) with that of step 5: (11.051763673 + 11.1837353437)/2 = 11.1177495084 (new guess).

Error = new guess - previous value = 11.1837353437 - 11.1177495084 = 0.0659858353.

0.0659858353 > 0.001. As error > accuracy, we repeat this step again.

Step 7:

Divide 123.6 by the previous result. d = 123.6/11.1177495084 = 11.1173578705.

Average this value (d) with that of step 6: (11.1173578705 + 11.1177495084)/2 = 11.1175536894 (new guess).

Error = new guess - previous value = 11.1177495084 - 11.1175536894 = 0.000195819.

0.000195819 <= 0.001. As error <= accuracy, we stop the iterations and use 11.1175536894 as the square root.

So, we can say that the square root of 123.6 is 11.117 with an error smaller than 0.001 (in fact the error is 0.000195819). this means that the first 3 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(123.6)' is 11.117553687749837

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