Square Root of A Number Online Calculator

The square root of a number is a value that, when multiplied by itself, gives the original number. This concept is fundamental in mathematics and has applications in various fields including geometry, algebra, and physics. Our online calculator makes it easy to find square roots quickly and accurately.

What is the Square Root?

The square root of a number is a mathematical operation that finds a number which, when multiplied by itself, equals the original number. For example, the square root of 16 is 4 because 4 × 4 = 16. Square roots are denoted by the radical symbol √ followed by the number.

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

Calculating square roots can be done using several methods:

Prime Factorization Method: Break down the number into its prime factors, then pair the factors and take one from each pair.
Long Division Method: Use a process similar to long division to find the square root.
Using a Calculator: The quickest method, especially for complex numbers.

Our online calculator uses a precise algorithm to compute square roots quickly and accurately.

Square Root Formula

The square root of a number x is written as √x. The formula is:

√x = y, where y × y = x

The square root function is the inverse of the squaring function. It's defined for non-negative real numbers and is a strictly increasing function.

Worked Examples

Example 1: Finding √25

To find the square root of 25:

Find a number that, when multiplied by itself, equals 25.
5 × 5 = 25, so √25 = 5.

Example 2: Finding √144

To find the square root of 144:

Find a number that, when multiplied by itself, equals 144.
12 × 12 = 144, so √144 = 12.

Frequently Asked Questions

What is the square root of a negative number?

The square root of a negative number is not a real number. It's an imaginary number, represented as √(-x) = i√x, where i is the imaginary unit (i² = -1).

Is the square root of a number always positive?

By convention, the principal (or positive) square root is used. However, both positive and negative roots exist for positive numbers, and only imaginary roots exist for negative numbers.

Can I use this calculator for complex numbers?

This calculator is designed for real numbers. For complex numbers, you would need a more advanced calculator that handles imaginary numbers.