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Square Root Calculator

Square Root Function:

\[ \sqrt{x} = y \text{ where } y^2 = x \]

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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:

\[ \sqrt{x} = y \text{ where } y^2 = x \]

Where:

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

3. Applications of Square Roots

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

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: This calculator only handles real numbers. For negative numbers, you would need complex numbers (using imaginary unit i).

Q2: How precise are the results?
A: Results are accurate to at least 4 decimal places.

Q3: What's the square root of 0?
A: The square root of 0 is 0.

Q4: What's the difference between √x and x^(1/2)?
A: They are mathematically equivalent - both represent the square root of x.

Q5: How are square roots calculated in computers?
A: Computers typically use iterative numerical methods like Newton's method to approximate square roots.

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