Question

root 1.8 with explanation​

Answer 1

Step-by-step explanation:

So, we can say that the square root of 1.8 is 1.34164 with an error smaller than 0.001 (in fact the error is 0.0000060911). this means that the first 5 decimal places are correct. Just to compare, the returned value by using the javascript function 'Math. sqrt(1.8)' is 1.3416407864998738.

Answer 2

Answer:

Step 1:

Divide the number (1.8) by 2 to get the first guess for the square root .

First guess = 1.8/2 = 0.9.

Step 2:

Divide 1.8 by the previous result. d = 1.8/0.9 = 2.

Average this value (d) with that of step 1: (2 + 0.9)/2 = 1.45 (new guess).

Error = new guess - previous value = 0.9 - 1.45 = 0.55.

0.55 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 1.8 by the previous result. d = 1.8/1.45 = 1.2413793103.

Average this value (d) with that of step 2: (1.2413793103 + 1.45)/2 = 1.3456896552 (new guess).

Error = new guess - previous value = 1.45 - 1.3456896552 = 0.1043103448.

0.1043103448 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 1.8 by the previous result. d = 1.8/1.3456896552 = 1.3376040999.

Average this value (d) with that of step 3: (1.3376040999 + 1.3456896552)/2 = 1.3416468776 (new guess).

Error = new guess - previous value = 1.3456896552 - 1.3416468776 = 0.0040427776.

0.0040427776 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 1.8 by the previous result. d = 1.8/1.3416468776 = 1.3416346954.

Average this value (d) with that of step 4: (1.3416346954 + 1.3416468776)/2 = 1.3416407865 (new guess).

Error = new guess - previous value = 1.3416468776 - 1.3416407865 = 0.0000060911.

0.0000060911 <= 0.001. As error <= accuracy, we stop the iterations and use 1.3416407865 as the square root.

So, we can say that the square root of 1.8 is 1.34164

Hope it helps

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