Calculate the square root of any number. Supports positive numbers, perfect squares detection, and decimal precision. Free online √ calculator.
The Square Root Calculator finds the square root of any non-negative number. The square root of x is the number that, when multiplied by itself, gives x. For example, √25 = 5 because 5 × 5 = 25.
Square roots appear throughout mathematics, science, and engineering: calculating distances (Pythagorean theorem), standard deviations in statistics, signal processing, and geometric calculations. This tool provides precise results and indicates whether the input is a perfect square.
The calculator handles perfect squares (giving exact integers), non-perfect squares (giving decimal results), and very large numbers. It also shows the squared value for verification.
This measurement provides a critical foundation for goal setting and progress tracking, helping you align daily activities with longer-term objectives and meaningful milestones. Integrating this calculation into regular planning habits ensures that work priorities reflect actual data about where time and energy produce the greatest results each week.
This measurement provides a critical foundation for goal setting and progress tracking, helping you align daily activities with longer-term objectives and meaningful milestones.
While simple square roots like √9 = 3 are easy, roots of non-perfect squares require computation. This tool provides precise results for any value. Consistent measurement creates a reliable baseline for evaluating personal efficiency and identifying the habits and practices that contribute most to achieving professional goals. Regular monitoring of this value helps individuals and teams detect productivity patterns and adjust workflows before small inefficiencies become entrenched and hard to correct.
√x = x^(1/2) The result r satisfies: r × r = x Perfect square: if r is a whole number
Result: 12
√144 = 12. Since 12 × 12 = 144, and 12 is a whole number, 144 is a perfect square.
The Pythagorean theorem, distance formula, and circle equations all involve square roots. Computing distances between points, finding diagonal lengths, and solving quadratic equations are everyday applications.
For mental math, bracket the number between two perfect squares. √50 is between 7 (√49) and 8 (√64). Since 50 is much closer to 49, √50 ≈ 7.07.
In statistics, standard deviation is the square root of variance. This makes it one of the most frequently used mathematical operations in data analysis.
Mastering this concept provides a strong foundation for advanced coursework in mathematics, statistics, and related quantitative disciplines.
The square root of a number x is a value r such that r² = x. Every positive number has two square roots: one positive and one negative. By convention, √ refers to the positive root.
Not in real numbers. The square root of a negative number is an imaginary number. For example, √(-4) = 2i, where i is the imaginary unit. This calculator handles non-negative inputs.
A perfect square is a number whose square root is an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. They are squares of 1, 2, 3, 4, ... respectively.
No. √2 is irrational, meaning it cannot be expressed as a fraction of two integers. Its decimal expansion (1.41421356...) never terminates or repeats.
In a right triangle with legs a and b, the hypotenuse c = √(a² + b²). For a 3-4-5 triangle: c = √(9+16) = √25 = 5.
Factor out perfect squares. √72 = √(36×2) = 6√2. Find the largest perfect square factor and take its root outside the radical.