Sqaure Roots Calculator

Square roots are fundamental in mathematics and have applications in geometry, algebra, and real-world measurements. This calculator provides an easy way to find square roots of numbers, along with an explanation of the underlying mathematics.

What is a square root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16. Square roots are denoted by the radical symbol √.

Square roots can be calculated for both perfect squares (numbers like 16, 25, 36) and non-perfect squares (numbers like 2, 3, 5). For non-perfect squares, the result is an irrational number that cannot be expressed as a simple fraction.

How to calculate square roots

There are several methods to calculate square roots:

Prime factorization method: Break down the number into its prime factors and pair them to find the square root.
Long division method: A more complex method that approximates the square root through successive divisions.
Using a calculator: The quickest method for most practical purposes.

The calculator on this page uses JavaScript to compute square roots with high precision, handling both perfect and non-perfect squares.

Square root formula

√x = y where y × y = x

The square root of a number x is a number y such that when y is multiplied by itself, the result is x. This relationship is fundamental in algebra and geometry.

Worked examples

Example 1: Perfect square

Find the square root of 36.

Solution: √36 = 6 because 6 × 6 = 36.

Example 2: Non-perfect square

Find the square root of 2.

Solution: √2 ≈ 1.41421356237 because 1.41421356237 × 1.41421356237 ≈ 2.

Example 3: Using the calculator

Enter 49 in the calculator and click "Calculate". The result will be 7, since 7 × 7 = 49.

FAQ

What is the difference between a square root and a square?: 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 squared, gives the original number (e.g., √25 = 5).
Can square roots be negative?: In real numbers, the principal (or non-negative) square root is used. For example, √9 = 3, not -3. However, in complex numbers, square roots can have negative values.
How accurate are the results from this calculator?: The calculator uses JavaScript's Math.sqrt() function, which provides results with approximately 15 decimal digits of precision. For most practical purposes, this is more than sufficient.
Can I use this calculator for scientific calculations?: Yes, this calculator is suitable for general mathematical calculations. For more advanced scientific calculations, you may need specialized software.
Is there a mobile app version of this calculator?: Currently, this calculator is available as a web application. We are working on developing a mobile app version that will be available in the near future.