Square Root Calculator

What Is a Square Root?

The square root of a number n is a value x such that x² = n. Written as √n, it is the inverse operation of squaring. Example: √144 = 12 because 12 × 12 = 144.

Perfect Squares vs. Irrational Roots

Numbers like 4, 9, 16, 25 have exact whole-number square roots called perfect squares. Most other numbers produce irrational results — √2 ≈ 1.41421356… — which go on forever without repeating.

How to Calculate Square Roots Manually

The digit-by-digit method and the Newton-Raphson method can approximate square roots by hand. However, for practical use, our calculator gives you an exact decimal result instantly.

Applications

Square roots appear in the Pythagorean theorem (a² + b² = c²), area calculation (side = √area), physics (RMS velocity), and statistics (standard deviation). They are also the basis of fractional exponents.