Online Square Root Calculator Radical

This online square root calculator helps you find the square root of any positive number. Whether you're working with radical notation or decimal approximations, our tool provides accurate results and explains 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 roots of 9 are 3 and -3 because 3 × 3 = 9 and (-3) × (-3) = 9.

Square roots are fundamental in mathematics, physics, engineering, and many other fields. They appear in calculations involving areas, distances, and other geometric measurements.

Square Root Formula:

√a = b, where b × b = a

How to Calculate Square Roots

There are several methods to calculate square roots:

Prime Factorization: Break down the number into its prime factors and pair them.
Long Division Method: A traditional algorithm for finding square roots.
Using a Calculator: The quickest and most accurate method for most practical purposes.

For non-perfect squares, calculators typically provide decimal approximations. For example, √2 ≈ 1.414213562.

Radical Notation

Radical notation uses the symbol √ (the radical sign) to represent square roots. The number under the radical is called the radicand.

Examples of radical notation:

√9 = 3
√16 = 4
√2 ≈ 1.414213562

For more complex expressions, you can use exponents: √a = a^(1/2).

Examples

Let's look at some examples of square roots:

Number	Square Root (Radical)	Square Root (Decimal)
4	√4 = 2	2.000000000
9	√9 = 3	3.000000000
16	√16 = 4	4.000000000
25	√25 = 5	5.000000000
2	√2	1.414213562

FAQ

What is the difference between a square root and a square?

The square of a number is the result of multiplying the number by itself (e.g., 3² = 9). The square root is the inverse operation that finds a number which, when multiplied by itself, gives the original number (e.g., √9 = 3).

Can I find the square root of a negative number?

In real numbers, the square root of a negative number is not defined. However, in complex numbers, negative square roots exist and involve the imaginary unit i (e.g., √-1 = i).

How accurate are the results from this calculator?

This calculator provides results with up to 15 decimal places for precision. For most practical purposes, fewer decimal places are sufficient.

Can I use this calculator for scientific calculations?

Yes, this calculator is suitable for scientific, engineering, and mathematical applications where square root calculations are needed.