Square Root Calculator

Online square root calculator. Calculate the square root of x.

The square root of x is given by the formula:

√x = r

Enter the input number (x) and press the  =  button:

√

 

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Square Root Calculator

Square root calculator helps you find the square root of any positive number.In some situations, you don't need to know the exact result of the square root. If this is the case, our square root calculator is the best option to estimate the value of every square root you desired. For example, let's say you want to know whether 4√5 is greater than 9. From the calculator, you know that √5 ≈ 2.23607, so 4√5 ≈ 4 * 2.23607 = 8.94428. It is very close to the 9, but it isn't greater than it! The square root calculator gives the final value with relatively high accuracy.

Square root definition

In mathematics, the traditional operations on numbers are addition, subtraction, multiplication, and division. Nonetheless, we sometimes add to this list some more advanced operations and manipulations: square roots, exponentiation, logarithmic functions and even trigonometric functions (e.g., sine and cosine). In this article, we will focus on the square root definition only.

The square root of a given number x is every number y whose square y² = y*y yields the original number x. Therefore, the square root formula can be expressed as:

√x = y ⟺ x = y²,

where ⟺ is a mathematical symbol that means if and only if. Each positive real number always has two square roots - the first is positive and second is negative. However, for many practical purposes, we usually use the positive one. The only number that has one square root is zero. It is because √0 = 0 and zero is neither positive nor negative.

There is also another common notation of square roots that could be more convenient in many complex calculations. This alternative square root formula states that the square root of a number is a number raised to the exponent of the fraction one half:

√x = x^(1/2) = x^(0.5)

In geometric interpretation, the square root of a given area of a square gives the length of its side. That's why √ has word square in its name. A similar situation is with the cube root ∛. If you take the cube root of the volume of a cube, you get the length of its edges. While square roots are used when considering surface areas, cube roots are useful to determine quantities that relate to the volume, e.g., density.