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This paper presents a new algorithm to approximate the nth root of a given real number  z . The proposed algorithm is a hybrid algorithm between the Bisection method and the combination of the inverse of sine series and Newton’s method. The proposed algorithm will be tested to find the numerical results on Matlab programming. The results showed that if  z  &gt; 1, the proposed method converges with the initial interval [1,  z ] and if 0 &lt;  z  &lt; 1, it converges with initial interval [0,4]. The comparison of the obtained result with Newton’s method and AS-Newton’s method shown that the efficiency of the proposed algorithm may better than both of them concerning the initial value.

A New Hybrid Algorithm of Bisection and Modified Newton’s Method for the nth root-finding of a Real Number