1. What is Square Root Simplification?

Square root simplification is the process of breaking down a square root into its simplest radical form by factoring out perfect squares from the radicand (the number under the square root symbol).

2. How Does the Calculator Work?

The calculator uses the property of radicals:

Where:

• \( a \) — A perfect square factor
• \( b \) — The remaining factor

Explanation: The calculator factors the input number, identifies perfect square factors, and moves them outside the square root symbol.

3. Importance of Simplifying Radicals

Details: Simplified radicals are easier to work with in algebraic operations, comparisons, and provide a standardized form for mathematical expressions.

4. Using the Calculator

Tips: Enter any positive integer greater than 0. The calculator will return the simplified radical form by factoring out perfect squares.

5. Frequently Asked Questions (FAQ)

Q1: What is a perfect square?
A: A perfect square is an integer that is the square of another integer (e.g., 1, 4, 9, 16, 25, etc.).

Q2: Why can't we simplify √13?
A: Because 13 is a prime number and has no perfect square factors other than 1.

Q3: How do you simplify √72?
A: √72 = √(36×2) = √36 × √2 = 6√2.

Q4: What's the difference between √50 and 5√2?
A: They are equivalent expressions, but 5√2 is the simplified form of √50.

Q5: Can all square roots be simplified?
A: No, square roots of prime numbers and numbers without perfect square factors (other than 1) cannot be simplified further.