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Simplifying Square Roots Calculator

Square Root Simplification Formula:

\[ \sqrt{a} = \sqrt{p \times q} = \sqrt{p} \times \sqrt{q} \]

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1. What is a Square Root Simplification Calculator?

Definition: This calculator simplifies square roots by factoring out perfect squares from the radicand (the number under the square root).

Purpose: It helps students and professionals express square roots in their simplest radical form, making mathematical expressions cleaner and easier to work with.

2. How Does the Calculator Work?

The calculator uses the mathematical property:

\[ \sqrt{a} = \sqrt{p \times q} = \sqrt{p} \times \sqrt{q} \]

Where:

Explanation: The calculator finds the largest perfect square that divides the input number, then expresses the square root as the product of the square root of that perfect square and the remaining square root.

3. Importance of Simplifying Square Roots

Details: Simplified radical forms are easier to work with in algebraic operations, comparisons, and provide exact values rather than decimal approximations.

4. Using the Calculator

Tips: Enter any positive integer greater than 0. The calculator will return the simplified radical form or the original square root if it cannot be simplified further.

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 √7?
A: Because 7 has no perfect square factors other than 1, so √7 is already in its simplest form.

Q3: How would √50 be simplified?
A: √50 = √(25×2) = 5√2, since 25 is the largest perfect square factor of 50.

Q4: What about simplifying √72?
A: √72 = √(36×2) = 6√2, as 36 is the largest perfect square factor of 72.

Q5: Can this calculator handle variables?
A: No, this version only works with numerical inputs. For algebraic expressions with variables, you would need a more advanced calculator.

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