Question

Find square root of 24.6 step by step

Answer 1

Answer:

The square root of 24.6 is 4.9598387070549.

Step-by-step explanation:

Step 1:

Divide the number (24.6) by 2 to get the first guess for the square root .

First guess = 24.6/2 = 12.3.

Step 2:

Divide 24.6 by the previous result. d = 24.6/12.3 = 2.

Average this value (d) with that of step 1: (2 + 12.3)/2 = 7.15 (new guess).

Error = new guess - previous value = 12.3 - 7.15 = 5.15.

5.15 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 24.6 by the previous result. d = 24.6/7.15 = 3.4405594406.

Average this value (d) with that of step 2: (3.4405594406 + 7.15)/2 = 5.2952797203 (new guess).

Error = new guess - previous value = 7.15 - 5.2952797203 = 1.8547202797.

1.8547202797 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 24.6 by the previous result. d = 24.6/5.2952797203 = 4.6456469345.

Average this value (d) with that of step 3: (4.6456469345 + 5.2952797203)/2 = 4.9704633274 (new guess).

Error = new guess - previous value = 5.2952797203 - 4.9704633274 = 0.3248163929.

0.3248163929 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 24.6 by the previous result. d = 24.6/4.9704633274 = 4.9492367974.

Average this value (d) with that of step 4: (4.9492367974 + 4.9704633274)/2 = 4.9598500624 (new guess).

Error = new guess - previous value = 4.9704633274 - 4.9598500624 = 0.010613265.

0.010613265 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 24.6 by the previous result. d = 24.6/4.9598500624 = 4.9598273517.

Average this value (d) with that of step 5: (4.9598273517 + 4.9598500624)/2 = 4.9598387071 (new guess).

Error = new guess - previous value = 4.9598500624 - 4.9598387071 = 0.0000113553.

0.0000113553 <= 0.001. As error <= accuracy, we stop the iterations and use 4.9598387071 as the square root.

So, we can say that the square root of 24.6 is 4.9598 with an error smaller than 0.001 (in fact the error is 0.0000113553). this means that the first 4 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(24.6)' is 4.959838707054898

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