Question

According to Newton-Raphson method, the value of \(\sqrt{12}\) up to three places of decimal will be

• A. 3.463
• B. 3.462
• C. 3.467
• D. None of these

Hint:

Use Newton-Raphson for fast square root approximation: \(x_{n+1} = \frac{1}{2}(x_n + \frac{N}{x_n})\).

Answer 1

The Correct Option is D

Concept: Newton-Raphson method: \[ x_{n+1} = \frac{1}{2}\left(x_n + \frac{12}{x_n}\right) \]

Step 1: Take initial approximation.
\[ x_0 = 3.5 \]

Step 2: Iterate.
\[ x_1 = \frac{1}{2}\left(3.5 + \frac{12}{3.5}\right) = 3.4643 \]

Step 3: Final value.
\[ \sqrt{12} \approx 3.464 \]

Step 4: Compare.
None of the options match exactly.