1. What is Square Root?

The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9.

2. How Does the Calculator Work?

The calculator uses the square root formula:

Where:

• \( x \) — The number you want to find the square root of (must be ≥ 0)
• \( y \) — The square root result

Explanation: The calculator uses PHP's built-in sqrt() function which provides accurate square root calculations.

3. Importance of Square Roots

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

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate square roots of negative numbers?
A: Not with real numbers. The square root of a negative number involves imaginary numbers (i).

Q2: What's the square root of 0?
A: The square root of 0 is 0 (0 × 0 = 0).

Q3: How precise are the results?
A: Results are accurate to at least 4 decimal places.

Q4: What's the difference between √ and ½ exponent?
A: Mathematically, √x is the same as x^(1/2). Both represent the square root.

Q5: How are square roots calculated without a calculator?
A: Methods include prime factorization (for perfect squares) or the long division method for arbitrary precision.