Square Root Kalkulator
Calculate the square root of any number instantly. Also shows cube root and nth root calculations.
Cara menggunakan kalkulator ini
- Masukkan Number
- Klik tombol Hitung
- Baca hasil yang ditampilkan di bawah kalkulator
What Is a Square Root?
The square root of a number n is the value that, when multiplied by itself, gives n. Written as √n, it is the inverse operation of squaring. For example, √25 = 5 because 5 × 5 = 25. Every positive number has two square roots: a positive and negative value (e.g., ±5 for 25), but by convention √n refers to the positive root.
Not all square roots are whole numbers. √2 = 1.41421..., √3 = 1.73205... — these are irrational numbers. This calculator gives you decimal-precision square roots instantly, along with cube roots and nth roots.
| Number (n) | √n (Square Root) | ∛n (Cube Root) |
|---|---|---|
| 1 | 1.000 | 1.000 |
| 4 | 2.000 | 1.587 |
| 9 | 3.000 | 2.080 |
| 16 | 4.000 | 2.520 |
| 25 | 5.000 | 2.924 |
| 50 | 7.071 | 3.684 |
| 100 | 10.000 | 4.642 |
| 144 | 12.000 | 5.241 |
| 256 | 16.000 | 6.350 |
Square Roots in Sports Statistics and Running Data
Square roots appear naturally in sports science and running analysis. Standard deviation — a key measure of consistency in training paces — is calculated using a square root. The formula: σ = √(Σ(x - x̄)² / n), where x̄ is the mean pace and n is the number of data points.
The Riegel race predictor formula also involves exponents: T2 = T1 × (D2/D1)^1.06. While not a simple square root, this fractional exponent is calculated using the same mathematical principles. Understanding roots and powers helps you interpret sports science literature and verify calculator outputs.
In geometry, square roots are needed for diagonal calculations (Pythagorean theorem: c = √(a² + b²)), useful for GPS-based route planning and elevation profile analysis on running apps.
Terakhir diperbarui: March 2026
Frequently Asked Questions
What is the square root of 2?
√2 = 1.41421356... This irrational number is fundamental in geometry (the diagonal of a unit square) and appears in many scientific and mathematical calculations.
How do I calculate a square root by hand?
Use the long division method or Newton's method: start with an estimate, divide n by the estimate, average the result with the estimate, and repeat. For example, √50: guess 7, then (7 + 50/7)/2 = (7 + 7.14)/2 = 7.07. One more iteration gives 7.0711.
What is the square root of a negative number?
The square root of a negative number is an imaginary number. √(-1) = i, the imaginary unit. √(-16) = 4i. Complex numbers involving imaginary roots are used in electrical engineering and quantum physics but rarely in everyday calculations.
How is the square root used in standard deviation?
Standard deviation = √(variance). You calculate variance by finding the mean of squared differences from the average, then take its square root. This is used in running to measure the consistency of training paces — a low standard deviation means very consistent splits.