1. What is Square Root of a Fraction?

The square root of a fraction is equal to the fraction of the square roots of the numerator and denominator. This property allows simplification of complex fractional expressions.

2. How Does the Calculator Work?

The calculator uses the mathematical property:

Where:

• \( a \) — Numerator (must be ≥0)
• \( b \) — Denominator (must be >0)

Explanation: The calculator first calculates the square root of the fraction directly, then verifies the result by calculating the ratio of the individual square roots.

3. Mathematical Explanation

Details: This property comes from the fundamental laws of exponents and roots. For any non-negative real numbers a and b (with b ≠ 0), the square root of their quotient equals the quotient of their square roots.

4. Using the Calculator

Tips: Enter the numerator and denominator values. The numerator must be ≥0 and denominator must be >0. The calculator will show both forms of the solution.

5. Frequently Asked Questions (FAQ)

Q1: Can I use negative numbers?
A: No, the numerator must be ≥0 (square root of negative numbers is complex) and denominator must be >0 (division by zero is undefined).

Q2: Does this work for other roots (cube roots, etc.)?
A: Yes, the same property applies to any nth root: the nth root of a fraction equals the fraction of the nth roots.

Q3: Why are there two results shown?
A: The calculator shows both the direct calculation and the separated calculation to demonstrate the mathematical equivalence.

Q4: How precise are the results?
A: Results are calculated with floating point precision (about 15-17 significant digits).

Q5: Can this be used for algebraic expressions?
A: The same principle applies to algebraic expressions, but this calculator only handles numerical values.