1. What is the Square Root Equation?

The square root equation \( x = \pm\sqrt{c} \) finds all real numbers x that satisfy \( x^2 = c \). For positive numbers, there are two real solutions (positive and negative roots). For zero, there's one solution (zero), and for negative numbers, there are no real solutions.

2. How Does the Calculator Work?

The calculator uses the square root equation:

Where:

• \( x \) — Solution(s) to the equation
• \( c \) — The value under the square root (radicand)

Explanation: The calculator computes both the positive and negative square roots when they exist in the real number system.

3. Importance of Square Root Calculation

Details: Square roots are fundamental in mathematics, physics, engineering, and many scientific calculations. They appear in quadratic equations, distance formulas, and various physical laws.

4. Using the Calculator

Tips: Enter any real number (positive, zero, or negative). The calculator will show both roots for positive numbers, one root for zero, and indicate no real solutions for negative numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why are there two solutions for positive numbers?
A: Because both a positive and negative number squared will give the same positive result (e.g., 2² = 4 and (-2)² = 4).

Q2: What about imaginary numbers?
A: For negative inputs, the solutions would be imaginary numbers (involving i = √-1), but this calculator shows only real number solutions.

Q3: How precise are the results?
A: Results are rounded to 4 decimal places for clarity, but calculations use full precision internally.

Q4: Can I calculate square roots of fractions?
A: Yes, enter the decimal equivalent or use the decimal point in your input.

Q5: What's the difference between √c and ±√c?
A: √c alone typically refers to the principal (positive) square root, while ±√c explicitly includes both solutions.