Question

Evaluate the square root of 0.6 by using long division method.

Answer 1

Answer:

Step 1:

Divide the number (0.6) by 2 to get the first guess for the square root .

First guess = 0.6/2 = 0.3.

Step 2:

Divide 0.6 by the previous result. d = 0.6/0.3 = 2.

Average this value (d) with that of step 1: (2 + 0.3)/2 = 1.15 (new guess).

Error = new guess - previous value = 0.3 - 1.15 = 0.85.

0.85 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 0.6 by the previous result. d = 0.6/1.15 = 0.5217391304.

Average this value (d) with that of step 2: (0.5217391304 + 1.15)/2 = 0.8358695652 (new guess).

Error = new guess - previous value = 1.15 - 0.8358695652 = 0.3141304348.

0.3141304348 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 0.6 by the previous result. d = 0.6/0.8358695652 = 0.7178153446.

Average this value (d) with that of step 3: (0.7178153446 + 0.8358695652)/2 = 0.7768424549 (new guess).

Error = new guess - previous value = 0.8358695652 - 0.7768424549 = 0.0590271103.

0.0590271103 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 0.6 by the previous result. d = 0.6/0.7768424549 = 0.772357376.

Average this value (d) with that of step 4: (0.772357376 + 0.7768424549)/2 = 0.7745999155 (new guess).

Error = new guess - previous value = 0.7768424549 - 0.7745999155 = 0.0022425394.

0.0022425394 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 0.6 by the previous result. d = 0.6/0.7745999155 = 0.774593423.

Average this value (d) with that of step 5: (0.774593423 + 0.7745999155)/2 = 0.7745966692 (new guess).

Error = new guess - previous value = 0.7745999155 - 0.7745966692 = 0.0000032463.

0.0000032463 <= 0.001. As error <= accuracy, we stop the iterations and use 0.7745966692 as the square root.

So, we can say that the square root of 0.6 is 0.77459 with an error smaller than 0.001 (in fact the error is 0.0000032463). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(0.6)' is 0.7745966692414834.

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Step-by-step explanation: