Question

Find the square root of 1.96 by prime factorisation method​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

1.4

Step-by-step explanation:

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

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