feat: add square root

DIRECTORY.md

@@ -124,6 +124,7 @@
       * [Hexagonal Numbers.Test](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/series/test/hexagonal_numbers.test.ts)
   * [Sieve Of Eratosthenes](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/sieve_of_eratosthenes.ts)
   * [Signum](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/signum.ts)
+  * [Square Root](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/square_root.ts)
   * [Ugly Numbers](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/ugly_numbers.ts)
   * [Zellers Congruence](https://github.com/TheAlgorithms/TypeScript/blob/HEAD/maths/zellers_congruence.ts)
 

maths/square_root.ts

@@ -0,0 +1,26 @@
+/**
+ * @function squareRoot
+ * @description Finding the square root of a number using Newton's method.
+ * @param {number} num - A number.
+ * @param {number} precision - Precision of square root, 1e-15 by default.
+ * @returns {number} - Square root of the given number.
+ * @see https://www.geeksforgeeks.org/find-root-of-a-number-using-newtons-method/
+ * @example SquareRoot(36) = 6
+ * @example SquareRoot(50) = 7.0710678118654755
+ */
+
+export const squareRoot = (num: number, precision: number = 1e-15): number => {
+  if (num < 0) throw new Error("number must be non-negative number");
+  if (num === 0) return 0;
+
+  let sqrt: number = num;
+  let curr: number;
+
+  while (true) {
+    curr = 0.5 * (sqrt + num / sqrt);
+    if (Math.abs(curr - sqrt) < precision) {
+      return sqrt;
+    }
+    sqrt = curr;
+  }
+};

maths/test/square_root.test.ts

@@ -0,0 +1,28 @@
+import { squareRoot } from "../square_root";
+
+describe("squareRoot", () => {
+  test.each([-1, -10, -2.4])(
+    "should throw an error for negative numbers",
+    (n: number) => {
+      expect(() => squareRoot(n)).toThrow("number must be non-negative number");
+    }
+  );
+
+  test.each([0, 1, 4, 9, 16, 25])(
+    "should return correct rational square root value",
+    () => {
+      (n: number) => {
+        expect(() => squareRoot(n)).toBeCloseTo(Math.sqrt(n));
+      };
+    }
+  );
+
+  test.each([2, 15, 20, 40, 99, 10032])(
+    "should return correct irrational square root value",
+    () => {
+      (n: number) => {
+        expect(() => squareRoot(n)).toBeCloseTo(Math.sqrt(n));
+      };
+    }
+  );
+});