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 function:

Where:

• \( x \) — Input number (must be ≥ 0)
• \( \sqrt{x} \) — Resulting square root

Explanation: The function calculates the principal (non-negative) square root of a non-negative real number.

3. Applications of Square Root

Details: Square roots are used in various fields including geometry (calculating side lengths), physics (root mean square calculations), statistics (standard deviation), and engineering.

4. Using the Calculator

Tips: Enter any non-negative number. The calculator will return its square root rounded 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 requires complex numbers (imaginary unit i).

Q2: What's the difference between √x and x^(1/2)?
A: They are mathematically equivalent. Both represent the square root of x.

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

Q4: What's the square root of 0?
A: The square root of 0 is 0 (0 × 0 = 0).

Q5: How are square roots calculated computationally?
A: Computers typically use iterative algorithms like Newton's method to approximate square roots.