Use Calculator to Find Square Root of Number

Finding the square root of a number is a fundamental mathematical operation with applications in geometry, algebra, and many other fields. This guide explains how to calculate square roots using our online calculator, including the formula, examples, and practical uses.

What is a Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For any non-negative real number x, the square root is written as √x. For example, the square root of 16 is 4 because 4 × 4 = 16.

Square roots can be either positive or negative, but by convention, the principal (or positive) square root is used unless specified otherwise. For example, √9 = 3, but both 3 and -3 are square roots of 9.

How to Calculate Square Root

There are several methods to calculate square roots, including:

Prime Factorization: Break down the number into its prime factors and pair them.
Long Division Method: A step-by-step process similar to long division.
Using a Calculator: The most practical method for most users.

Formula

The square root of a number x is a number y such that:

y × y = x

Or mathematically:

y = √x

Our calculator uses the built-in JavaScript Math.sqrt() function, which provides an accurate and efficient calculation.

Examples

Let's look at a few examples of calculating square roots:

√16 = 4 (since 4 × 4 = 16)
√25 = 5 (since 5 × 5 = 25)
√100 = 10 (since 10 × 10 = 100)
√2 = 1.41421356237 (approximately)

Note

For non-perfect squares, the calculator provides an approximate decimal value.

Applications

Square roots have many practical applications, including:

Geometry: Calculating lengths of sides in right triangles.
Algebra: Solving quadratic equations.
Physics: Calculating velocities and distances.
Finance: Determining standard deviations in statistics.
Computer Science: Used in algorithms and data compression.

FAQ

What is the difference between square and square root?: The square of a number is obtained by multiplying the number by itself (e.g., 5² = 25). The square root is the inverse operation that finds a number which, when multiplied by itself, gives the original number (e.g., √25 = 5).
Can the square root of a negative number be calculated?: In real numbers, no. The square root of a negative number is not defined. However, in complex numbers, negative numbers have square roots involving the imaginary unit i (e.g., √-1 = i).
How do I calculate the square root of a fraction?: The square root of a fraction is the fraction of the square roots. For example, √(1/4) = √1 / √4 = 1/2.
What is the square root of zero?: The square root of zero is zero, since 0 × 0 = 0.
How accurate is the calculator's square root calculation?: The calculator uses JavaScript's built-in Math.sqrt() function, which provides results accurate to approximately 15 decimal places.