Square Root Calculator
Calculate square roots with perfect square detection, decimal approximations, and step-by-step calculations. Perfect for algebra, geometry, and mathematical problem solving.
Square Root Calculator
Common Square Roots
Click on these links to see instant calculations with perfect squares:
Square Roots
A square root of a number is a value that, when multiplied by itself, gives the original number. Square roots are fundamental in algebra, geometry, and many mathematical applications.
Square Root Properties
√(ab) = √a × √b (for non-negative a, b)
√(a/b) = √a / √b (for non-negative a, positive b)
(√a)² = a (for non-negative a)
√0 = 0, √1 = 1
Perfect Squares
| Number | Square Root | Perfect Square | Calculation |
|---|---|---|---|
| 1 | 1 | Yes | 1² = 1 |
| 4 | 2 | Yes | 2² = 4 |
| 9 | 3 | Yes | 3² = 9 |
| 16 | 4 | Yes | 4² = 16 |
| 25 | 5 | Yes | 5² = 25 |
| 36 | 6 | Yes | 6² = 36 |
| 49 | 7 | Yes | 7² = 49 |
| 64 | 8 | Yes | 8² = 64 |
| 81 | 9 | Yes | 9² = 81 |
| 100 | 10 | Yes | 10² = 100 |
- Algebra: Solve quadratic equations and simplify radical expressions
- Geometry: Calculate distances, areas, and apply Pythagorean theorem
- Physics: Determine velocities, accelerations, and wave properties
- Engineering: Calculate magnitudes, RMS values, and design parameters
- Statistics: Compute standard deviations and variance calculations
Frequently Asked Questions
What is a square root?
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 25 is 5 because 5 × 5 = 25.
How do you calculate square roots?
Square roots can be calculated using various methods including prime factorization, long division, or approximation methods. For perfect squares, the result is a whole number.
What is a perfect square?
A perfect square is a number that is the square of an integer. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. Their square roots are whole numbers.