Square Root Calculator
Enter a number to compute its square root, cube root, reciprocal, and check for perfect squares
Square Root βn
4
β16 = 4 (perfect square: 4Β²)
Original Number
16
Perfect Square?
Yes β
1/βn
Cube Root β
βn Γ β2
Square Root Explained
The square root of a number is its second root. For example, the square root of 16 is 4 because 4Β² = 16. Mathematically written as β16 = 4.
Common Perfect Squares
| 1Β²=1 | 2Β²=4 | 3Β²=9 | 4Β²=16 | 5Β²=25 |
| 6Β²=36 | 7Β²=49 | 8Β²=64 | 9Β²=81 | 10Β²=100 |
| 11Β²=121 | 12Β²=144 | 13Β²=169 | 14Β²=196 | 15Β²=225 |
Real-World Applications of Square Roots
- Geometry: Side length from square area, radius from circle area
- Physics: Free-fall time t = β(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?
β16 = 4, because 4Β² = 16. 16 is a perfect square.
What is β2 approximately?
β2 β 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, β(-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' (βn), while cube root asks 'what number cubed equals n' (βn). For example, β64 = 8 but β64 = 4 (since 4Β³ = 64).