Free square root calculator with high precision results. Find the square root of any positive number instantly. Perfect for math, science, and engineering.
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Finding square roots doesn't have to be complicated. Our calculator instantly computes the square root of any positive number with high precision, perfect for students, engineers, and anyone working with mathematical calculations.
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9. Square roots are fundamental in geometry (calculating distances and areas), physics (wave equations), statistics (standard deviation), and many other fields. Every positive number has two square roots: one positive and one negative, though we typically refer to the positive root.
Mathematical Notation
√x = y, where y² = xGet square roots calculated to many decimal places for accurate scientific and engineering work.
Works with any positive number, whether it's a perfect square like 16 or an imperfect square like 7.
Learn whether your number is a perfect square and understand the mathematical relationship.
Calculate diagonal distances, determine side lengths from area, and solve Pythagorean theorem problems.
Compute standard deviations and root mean square values for data analysis.
Solve equations involving velocity, energy, electrical calculations, and wave mechanics.
Calculate volatility, risk metrics, and compound annual growth rates (CAGR).
A perfect square is a number whose square root is a whole number. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. Perfect squares result from multiplying an integer by itself.
In the real number system, negative numbers don't have real square roots because no real number multiplied by itself gives a negative result. However, in the complex number system, negative numbers have imaginary square roots. For example, √(-1) = i (the imaginary unit).
A cube root is a number that, when multiplied by itself three times, gives the original number. While our calculator focuses on square roots, cube roots can be calculated as x^(1/3). For example, the cube root of 27 is 3 because 3 × 3 × 3 = 27.
The square root of 2 (approximately 1.41421...) is irrational because it cannot be expressed as a simple fraction. Its decimal representation goes on forever without repeating. This was proven by ancient Greek mathematicians and is one of the most famous proofs in mathematics.