Square Root Calculator

Calculate square roots with step-by-step solutions, perfect square identification, and visual representations

✓ Instant calculations ✓ Perfect square detection ✓ Step-by-step solutions

Calculate Square Root

√

Perfect Squares

√1 1
√4 2
√9 3
√16 4
√25 5
√36 6
√49 7
√64 8
√81 9
√100 10

Square Root Properties

√(a × b) = √a × √b
√(a/b) = √a / √b
√a² = |a|
√0 = 0
√1 = 1
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Understanding Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. The square root symbol (√) is called a radical.

Definition

If √a = b, then b² = a

Perfect Squares

Perfect squares are numbers whose square roots are whole numbers. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Applications

Geometry

Finding the side length of a square when you know its area, or calculating distances using the Pythagorean theorem.

Physics

Calculating velocities, accelerations, and other physical quantities that involve squared relationships.

Statistics

Computing standard deviations and other statistical measures that involve square roots.

Engineering

Designing structures, calculating loads, and solving engineering problems involving quadratic relationships.