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
• \( \sqrt{x} \) — The square root of x

Explanation: The square root function is equivalent to raising the number to the power of 1/2.

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 calculator will return the principal (non-negative) square root.

5. Frequently Asked Questions (FAQ)

Q1: Can I calculate square roots of negative numbers?
A: The principal square root of a negative number is not a real number (it's an imaginary number). This calculator only works with real numbers (x ≥ 0).

Q2: What's the difference between √x and x^(1/2)?
A: They are mathematically equivalent. The √ notation is more common for square roots, while the exponent notation is more general and works for any root.

Q3: How precise are the results?
A: Results are accurate to 4 decimal places. For most practical purposes, this is sufficient precision.

Q4: What are some common square roots?
A: Some common perfect squares and their roots: √4 = 2, √9 = 3, √16 = 4, √25 = 5, √36 = 6, etc.

Q5: Can this calculator handle very large numbers?
A: Yes, within the limits of PHP's floating-point arithmetic. Extremely large numbers might lose some precision.