Square Root Calculator
Enter a number to compute its square root, cube root, reciprocal, and check for perfect squares
Square Root √n
4
√16 = 4 (perfect square: 4²)
Original Number
16
Perfect Square?
Yes ✓
1/√n
Cube Root ∛
√n × √2
Square Root Explained
The square root of a number is its second root. For example, the square root of 16 is 4 because 4² = 16. Mathematically written as √16 = 4.
Common Perfect Squares
| 1²=1 | 2²=4 | 3²=9 | 4²=16 | 5²=25 |
| 6²=36 | 7²=49 | 8²=64 | 9²=81 | 10²=100 |
| 11²=121 | 12²=144 | 13²=169 | 14²=196 | 15²=225 |
Real-World Applications of Square Roots
- Geometry: Side length from square area, radius from circle area
- Physics: Free-fall time t = √(2h/g)
- Statistics: Standard deviation is the square root of variance
- Engineering: Pythagorean theorem for hypotenuse calculation
FAQ
What is the square root of 16?
√16 = 4, because 4² = 16. 16 is a perfect square.
What is √2 approximately?
√2 ≈ 1.4142135624. It's an irrational number with infinite non-repeating decimals. When your calculator shows 1.414, that's rounded.
Can you take the square root of a negative number?
Not in real numbers. But in complex numbers, √(-1) = i (the imaginary unit). This calculator only supports non-negative real numbers.
What's the difference between square root and cube root?
Square root asks 'what number squared equals n' (√n), while cube root asks 'what number cubed equals n' (∛n). For example, √64 = 8 but ∛64 = 4 (since 4³ = 64).