Procedure to find qth root by N-R Method: Let, x = N 1 q , where q = 1, 2, 3, …… ,n and N is an natural number. ⇒x q - N = 0 ⇒fx = x q - N ⇒f'x =q x q-1 By the general formula we get, x n+1= 1 q q-1 xn + N x n q-1 Where, n = 0, 1, 2, 3, … To find the square root of 8 Let, x = 8 ⇒ x2 - 8 = 0 ⇒fx = x 2 - 8 ⇒f'x =2 x Let, x0 = 3 By N-R Method: x n+1 = 1 2 xn + N xn , n = 0, 1, 2, 3, ... x1 = 1 2 x 0 + 8 x 0 x1 = 1 2 3 + 8 3 x1 = 2.83 n x n+1 0 2.83 1 2.83 Therefore, x = 2.83 is the square root of 8.
