Square Root Calculator
Calculate square roots with detailed step-by-step solutions, perfect square identification, and explanations.
Enter Number
• Enter any non-negative number
• Perfect squares will show exact results
Result
Enter a non-negative number to calculate its square root
Square Root Properties
√(a × b) = √a × √b
√(a/b) = √a / √b
√(a²) = |a|
(√a)² = a (for a ≥ 0)
Perfect Squares
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
√121 = 11
√144 = 12
Examples
Perfect Squares
√25 = 5 (exact)
√64 = 8 (exact)
√100 = 10 (exact)
√169 = 13 (exact)
Non-Perfect Squares
√2 ≈ 1.414214
√3 ≈ 1.732051
√5 ≈ 2.236068
√10 ≈ 3.162278
Applications
Geometry
Finding side lengths in right triangles, areas, and distances
Physics
Calculating velocities, accelerations, and wave properties
Statistics
Standard deviation calculations and data analysis
Engineering
Structural calculations and signal processing
Frequently Asked Questions
A square root of a number x is a value that, when multiplied by itself, gives x. For example, the square root of 25 is 5 because 5 × 5 = 25.