Square Root (Floor √n) Explained | Brute Force ➜ Binary Search ➜ Math Trick (log/exp)

Find Floor Square Root FAST | O(√n) → O(log n) → O(1) Math Hack! Floor √n Explained | Binary Search + Math.log Trick + Full Proof Square Root Without Math.sqrt() | 3 Best Methods + Mathematical Proof! Given a positive integer n, find the square root of n. If n is not a perfect square, then return the floor value. Floor value of any number is the greatest Integer which is less than or equal to that number. In this lecture, we break down one of the fundamental DSA math problems: **Find the floor of the square root of a number**, without using Math.sqrt(). We start from scratch — pure mathematical intuition — and build up three powerful solutions: 1️⃣ Brute Force (O(√n)) 2️⃣ Binary Search (O(log n)) 3️⃣ Mathematical Trick using log/exp (O(1) in practice) Concepts You Will Learn Logarithms and exponentials as inverse functions Why ln(n)/2 → log space scaling of square root Proof that e^(ln n) = n Floating-point precision limits Using math identity to compute sqrt Binary Search monotonic property Integer overflow precautions using long Perfect For DSA preparation Interview math logic Students learning binary search Anyone building intuition for numerical algorithms Competitive programming #SquareRoot #DSA #MathLogicInCode #BinarySearch #ProgrammingTutorial #JavaCoding #MathTricks #CodingInterview square root algorithm, floor square root, sqrt without Math.sqrt, floor sqrt in java, find square root without sqrt, log exp sqrt trick, math.log math.exp sqrt, sqrt using logarithms, sqrt using binary search, sqrt brute force, floor square root explanation, square root derivation, sqrt using math identity, math logic in code, dsa math problems, binary search explained, sqrt correction floating point, e^(0.5 ln n), math exp log relationship, integer square root, fast square root, java square root implementation, sqrt without floating point, sqrt derivation proof, sqrt monotonic function, dynamic programming math, algorithm tutorial mathematical, coding interview questions sqrt