Square Root Calculator

What Is a Square Root?

A square root is a number that, when multiplied by itself, produces the original number. For example, the square root of 25 is 5 because 5 × 5 = 25.

The square root symbol is called the radical sign and is written as √. When no index is shown, √ represents the principal square root.

How to Use the Square Root Calculator

1. Enter a non-negative number.
2. Review the calculated square root.
3. Check whether the number is a perfect square.

The calculator accepts whole numbers and decimal values and displays the result with a practical number of decimal places.

Square Root Formula

The square root of a number x is written as:

√x = y

This means that y × y = x. For example, √64 = 8 because 8 × 8 = 64.

Perfect Squares

A perfect square is a non-negative integer that can be written as an integer multiplied by itself. Common perfect squares include 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100.

Perfect squares have whole-number square roots. For example, the square root of 144 is exactly 12.

Examples of Square Roots

• √1 = 1
• √4 = 2
• √9 = 3
• √16 = 4
• √25 = 5
• √100 = 10
• √144 = 12

Square Root of a Decimal

A square root does not have to be a whole number. For example, √2 is approximately 1.4142, while √10 is approximately 3.1623.

The calculator rounds the displayed result for readability, while the underlying calculation uses JavaScript's square-root function.

Can You Take the Square Root of a Negative Number?

In the real number system, the square root of a negative number is not defined. This calculator therefore accepts zero and positive numbers only.

In complex numbers, negative values can have square roots involving the imaginary unit i. Those calculations are outside the scope of this calculator.

Square Root vs. Squaring a Number

Squaring a number multiplies it by itself. Taking a square root reverses that operation for non-negative numbers.

For example, 7² = 49 and √49 = 7.

Worked Example

Suppose you need to calculate the square root of 225. Since 15 × 15 = 225, the square root is exactly 15.

For a number such as 50, the result is approximately 7.0711 because 50 is not a perfect square.

Square Roots in Everyday Calculations

Square roots are commonly used in mathematics, geometry, statistics, science, engineering, and financial calculations. They can also appear when solving equations where an unknown value has been squared.

Frequently Asked Questions