Question

Square root of 1.96 by divisible method

Answer 1

Answer:

Step 1:

Divide the number (1.96) by 2 to get the first guess for the square root .

First guess = 1.96/2 = 0.98.

Step 2:

Divide 1.96 by the previous result. d = 1.96/0.98 = 2.

Average this value (d) with that of step 1: (2 + 0.98)/2 = 1.49 (new guess).

Error = new guess - previous value = 0.98 - 1.49 = 0.51.

0.51 > 0.001. As error > accuracy, we repeat this step again.

Step 3:

Divide 1.96 by the previous result. d = 1.96/1.49 = 1.3154362416.

Average this value (d) with that of step 2: (1.3154362416 + 1.49)/2 = 1.4027181208 (new guess).

Error = new guess - previous value = 1.49 - 1.4027181208 = 0.0872818792.

0.0872818792 > 0.001. As error > accuracy, we repeat this step again.

Step 4:

Divide 1.96 by the previous result. d = 1.96/1.4027181208 = 1.3972871462.

Average this value (d) with that of step 3: (1.3972871462 + 1.4027181208)/2 = 1.4000026335 (new guess).

Error = new guess - previous value = 1.4027181208 - 1.4000026335 = 0.0027154873.

0.0027154873 > 0.001. As error > accuracy, we repeat this step again.

Step 5:

Divide 1.96 by the previous result. d = 1.96/1.4000026335 = 1.3999973665.

Average this value (d) with that of step 4: (1.3999973665 + 1.4000026335)/2 = 1.4 (new guess).

Error = new guess - previous value = 1.4000026335 - 1.4 = 0.0000026335.

0.0000026335 <= 0.001. As error <= accuracy, we stop the iterations and use 1.4 as the square root.

So, we can say that the square root of 1.96 is 1.4 with an error smaller than 0.001 (in fact the error is 0.0000026335).