PE-Nth root algorithm.ipynb

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    "# Python everything, exercise:\n",
    "## Nth root algorithm for computing $\\sqrt[n] a$\n",
    "**Nth root algorithm** computes the *nth root* of a given positive number $a$ by\n",
    " 1) $x_0 \\leftarrow$ some initial guess <br>\n",
    " 2) for $k=0,1,2...$ do: <br>\n",
    "$\\;\\;\\;\\;\\Large x_{k+1}=\\frac{1}{n}((n-1)x_k+\\frac{a}{x^{n-1}_k})$\n",
    "\n",
    "YouTube Channel: **@ostad-ai**\n",
    "<br>The Python code is at: https://github.com/ostad-ai/Python-Everything"
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    "def nth_root(a,n=2,x0=1,iter=20):\n",
    "    xk=x0\n",
    "    n1=n-1\n",
    "    for _ in range(iter):\n",
    "        xk=(n1*xk+a/xk**n1)/n\n",
    "    return xk"
   ]
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     "text": [
      "3th root of 2 is:1.2599210498948732\n"
     ]
    }
   ],
   "source": [
    "a=2\n",
    "n=3\n",
    "print(f'{n}th root of {a} is:{nth_root(a,n)}')"
   ]
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