Question

square root of long division method - 32.85​

Answer 1

Answer:

Step 1:

Divide the number (32.85) by 2 to get the first guess for the square root .

First guess = 32.85/2 = 16.425.

Step 2:

Divide 32.85 by the previous result. d = 32.85/16.425 = 2.

Average this value (d) with that of step 1: (2 + 16.425)/2 = 9.2125 (new guess).

Error = new guess - previous value = 16.425 - 9.2125 = 7.2125.

7.2125 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 32.85 by the previous result. d = 32.85/9.2125 = 3.565807327.

Average this value (d) with that of step 2: (3.565807327 + 9.2125)/2 = 6.3891536635 (new guess).

Error = new guess - previous value = 9.2125 - 6.3891536635 = 2.8233463365.

2.8233463365 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 32.85 by the previous result. d = 32.85/6.3891536635 = 5.1415260503.

Average this value (d) with that of step 3: (5.1415260503 + 6.3891536635)/2 = 5.7653398569 (new guess).

Error = new guess - previous value = 6.3891536635 - 5.7653398569 = 0.6238138066.

0.6238138066 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 32.85 by the previous result. d = 32.85/5.7653398569 = 5.6978427665.

Average this value (d) with that of step 4: (5.6978427665 + 5.7653398569)/2 = 5.7315913117 (new guess).

Error = new guess - previous value = 5.7653398569 - 5.7315913117 = 0.0337485452.

0.0337485452 > 0.001. As error > accuracy, we repeat this step again.

Step 6:

Divide 32.85 by the previous result. d = 32.85/5.7315913117 = 5.7313925947.

Average this value (d) with that of step 5: (5.7313925947 + 5.7315913117)/2 = 5.7314919532 (new guess).

Error = new guess - previous value = 5.7315913117 - 5.7314919532 = 0.0000993585.

0.0000993585 <= 0.001. As error <= accuracy, we stop the iterations and use 5.7314919532 as the square root.

So, we can say that the square root of 32.85 is 5.7314 with an error smaller than 0.001 (in fact the error is 0.0000993585). this means that the first 4 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math.sqrt(32.85)' is 5.73149195236284.

Step-by-step explanation:

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