Question

We want to compute the square root of 5 using the NR method. The square root of 5 is one of the solutions to the equation x^2-5=0. Using the NR method, write a script that computes the square root of 5 and check that your results are correct.

Answer 1

To compute the square root of 5 using the NR method, you can solve the equation x^2-5=0 using an iterative process. By updating a guess for the square root, you can reach an approximate value. A script to perform this computation is provided.

Step-by-step explanation:

To compute the square root of 5 using the Newton-Raphson (NR) method, we need to find the solution to the equation x^2 - 5 = 0. The NR method involves iteratively updating a guess for the square root until it converges to the actual square root. Here's a script to perform the computation:

x = 5 # initial guess

for i in range(10):
x = x - ((x ** 2 - 5) / (2 * x))

square_root = x
print(square_root)

Running this script will give you an approximate value for the square root of 5. You can check the accuracy of the result by squaring the computed square root and verifying that it is close to 5.