Sqaur Root Calculator

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 of positive real numbers quickly and accurately.

What is Square Root?

The square root of a number x is written as √x. It is the non-negative number that, when multiplied by itself, equals x. For example, the square root of 25 is 5 because 5 × 5 = 25.

Square roots are used in many mathematical applications, including geometry, algebra, and calculus. They are also essential in real-world problems involving areas, distances, and other measurements.

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 series of divisions to approximate the square root.
Using a Calculator: The most efficient method for most practical purposes.

Our square root calculator uses a precise algorithm to provide accurate results quickly.

Square Root Formula

For a non-negative real number x, the square root is defined as:

√x = y, where y × y = x and y ≥ 0

The square root function is the inverse of the squaring function. It is a strictly increasing function for x ≥ 0.

Square Root Examples

Example 1: √16

Find the square root of 16.

Solution: √16 = 4, because 4 × 4 = 16.

Example 2: √2

Find the square root of 2.

Solution: √2 ≈ 1.414213562, because 1.414213562 × 1.414213562 ≈ 2.

Square Root Table

Here's a table showing square roots of numbers from 1 to 20:

Number (x)	Square Root (√x)
1	1.000000
2	1.414214
3	1.732051
4	2.000000
5	2.236068
6	2.449490
7	2.645751
8	2.828427
9	3.000000
10	3.162278

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?: In real numbers, negative numbers do not have square roots. However, in complex numbers, the square root of a negative number is an imaginary number.
Is the square root of a number always positive?: Yes, by definition, the square root of a non-negative real number is always non-negative. The principal (or conventional) square root is the non-negative one.
How do I calculate the square root of a fraction?: The square root of a fraction a/b is √(a/b) = √a / √b. You can calculate the square roots of the numerator and denominator separately and then divide them.
What is the difference between square root and square?: The square of a number is that number multiplied by itself (x² = x × x). The square root is the inverse operation that finds a number which, when multiplied by itself, gives the original number (√x = y, where y × y = x).