Online Algebra Calculator Square Root

The square root of a number is a value that, when multiplied by itself, gives the original number. This calculator helps you find square roots quickly and accurately.

What is a Square Root?

The square root of a number x is a number y such that y² = x. For example, the square root of 16 is 4 because 4 × 4 = 16. Square roots are important in many areas of mathematics, including algebra, geometry, and calculus.

Every non-negative real number has exactly two square roots: one positive and one negative. For example, the square roots of 9 are 3 and -3. The principal (or positive) square root is usually denoted with the radical symbol √.

How to Calculate Square Roots

There are several methods to find square roots:

Prime Factorization: Break down the number into its prime factors, then pair the factors and take one from each pair.
Long Division Method: A more complex method that involves estimating and refining the square root.
Using a Calculator: The quickest method for most practical purposes.

Our online calculator uses a combination of these methods to provide accurate results quickly.

Square Root Formula

The square root of a number x can be represented as:

√x = y

where y × y = x

For example, √16 = 4 because 4 × 4 = 16.

Worked Examples

Example 1: Finding √25

We need to find a number that, when multiplied by itself, equals 25.

5 × 5 = 25, so √25 = 5.

Example 2: Finding √144

We need to find a number that, when multiplied by itself, equals 144.

12 × 12 = 144, so √144 = 12.

Example 3: Finding √2

This is an irrational number, so we can only approximate it.

√2 ≈ 1.414213562

Frequently Asked Questions

What is the square root of zero?: The square root of zero is zero, because 0 × 0 = 0.
Can negative numbers have square roots?: Yes, negative numbers can have square roots, but they are not real numbers. They are called imaginary numbers and are represented with the letter i, where i = √-1.
What is the difference between a square root and a square?: A square is a number multiplied by itself (e.g., 5² = 25). A square root is a number that, when multiplied by itself, gives the original number (e.g., √25 = 5).
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, √(a/b) = √a / √b.
What is the square root of a negative number?: The square root of a negative number is an imaginary number. For example, √-1 = i, where i is the imaginary unit.