1. What is Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. It's represented by the radical symbol (√) or as an exponent of 1/2.

2. How Does the Calculator Work?

The calculator uses the square root formula:

Where:

• \( n \) — Any non-negative real number
• \( \sqrt{n} \) — The principal (non-negative) square root

Explanation: The square root function is the inverse of squaring a number. For example, since 3² = 9, then √9 = 3.

3. Importance of Square Root Calculation

Details: Square roots are fundamental in mathematics and have applications in geometry, physics, engineering, statistics, and many other fields.

4. Using the Calculator

Tips: Enter any non-negative number to calculate its square root. The result will be rounded to 4 decimal places.

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate square roots of negative numbers?
A: Not with real numbers. Negative numbers have complex square roots (using imaginary unit i).

Q2: What's the difference between principal and negative square root?
A: Every positive number has two square roots (e.g., √9 = 3 and -3). The calculator shows only the principal (non-negative) root.

Q3: How is square root related to exponents?
A: Square root is equivalent to raising a number to the power of 1/2 (n^(1/2)).

Q4: What are perfect squares?
A: Numbers whose square roots are integers (e.g., 1, 4, 9, 16, 25, etc.).

Q5: How accurate is this calculator?
A: It provides results accurate to 4 decimal places using PHP's sqrt() function.