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 mathematical square root function:

Where:

• \( x \) — The input number (must be ≥ 0)
• \( y \) — The result where \( y × y = x \)

Explanation: The calculator computes the principal (non-negative) square root using PHP's sqrt() function and determines whether it's a perfect square.

3. Perfect vs Imperfect Squares

Details: Perfect squares are integers that are squares of other integers (e.g., 16, 25). All other positive numbers have irrational square roots that must be approximated.

4. Using the Calculator

Tips: Enter any non-negative number. The calculator will show whether the result is exact (for perfect squares) or approximate.

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate square roots of negative numbers?
A: No, the calculator only handles non-negative real numbers. Negative numbers have complex square roots.

Q2: How precise are the approximations?
A: Results are rounded to 4 decimal places by default. The actual calculation uses PHP's precision.

Q3: What's the largest number I can enter?
A: The calculator can handle numbers up to PHP's floating-point maximum (about 1.8e308).

Q4: Why does it say "perfect square" for some results?
A: This indicates the number is the square of an integer (e.g., 144 is 12×12).

Q5: How is this different from other root calculations?
A: This specifically calculates the square root (2nd root). Other roots (cube, etc.) require different calculations.