Square Root Calculator — Instant Results with Step-by-Step Solutions

What is a Square Root?

A square root of a number is a value that, when multiplied by itself, gives the original number, written using the radical symbol √. For example, √144 = 12, because 12 × 12 = 144. Use our square root calculator above to find the square root of any number in seconds.

How to Calculate Square Root Step by Step?

Method 1 — Perfect Squares Step 1: Check if the number is a perfect square (1, 4, 9, 16, 25, 36…). Step 2: Find the number that multiplied by itself gives your number. Step 3: That number is your square root. Example: √81 = 9, because 9 × 9 = 81. Method 2 — Long Division Method Step 1: Group digits in pairs from right to left. Step 2: Find the largest number whose square is less than or equal to the first group.

Where Are Square Roots Used in Real Life?

Geometry: The Pythagorean theorem (a² + b² = c²) uses square roots to find the hypotenuse of a right triangle. Physics: Speed, energy, and wave calculations use square root formulas. Finance: Volatility and standard deviation markets are calculated using square roots. Architecture: Structural load calculations and diagonal measurements require square roots.