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The Square Root Calculator is a straightforward tool designed to find the square root of any non-negative number. A square root of a number 'x' is a number 'y' such that y² = x.

√ How It Works

To use the calculator:

• Enter a Number: Input any non-negative number (integers or decimals) into the field under the square root symbol (√).
• Calculate: Click the "Calculate" button.

The calculator will then display the principal (non-negative) square root of the number you entered. If you enter a negative number, the calculator will indicate an error, as the real square root of a negative number is undefined.

Frequently Asked Questions (FAQ)

What is a 'principal' square root?

Every positive number has two square roots: one positive and one negative (e.g., both 4 and -4 when squared equal 16). The principal square root is the non-negative root, which is the one this calculator provides.

Why can't I calculate the square root of a negative number?

In the system of real numbers, multiplying any number (positive or negative) by itself always results in a positive number. Therefore, there is no real number that can be squared to produce a negative result. This requires the use of imaginary numbers (e.g., √-1 = i), which is a topic in advanced algebra.

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

A square root of x is a number that, when squared (y²), equals x. A cube root of x is a number that, when cubed (y³), equals x. You can find cube roots using our Cube Root Calculator.

What are some common uses for square roots?

Square roots are fundamental in many areas. They are used in geometry to find the side of a square from its area or in the Pythagorean theorem (a² + b² = c²). In physics, they appear in formulas for distance and velocity. In statistics, they are used to calculate the standard deviation.