1. What is the Square Root Fraction?

The square root of a fraction equals the fraction of the square roots. This mathematical property allows simplification of complex expressions and is fundamental in algebra and calculus.

2. How Does the Calculator Work?

The calculator demonstrates the mathematical identity:

Where:

• \( a \) — Numerator (non-negative number)
• \( b \) — Denominator (positive number)

Explanation: The calculator shows both sides of the equation to demonstrate their equality for any valid input values.

3. Mathematical Proof

Proof: \[ \left(\frac{\sqrt{a}}{\sqrt{b}}\right)^2 = \frac{(\sqrt{a})^2}{(\sqrt{b})^2} = \frac{a}{b} \] Therefore, \(\frac{\sqrt{a}}{\sqrt{b}}\) must be the square root of \(\frac{a}{b}\).

4. Using the Calculator

Tips: Enter any non-negative numerator and positive denominator. The calculator will show both forms of the calculation to demonstrate their equivalence.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for negative numbers?
A: The numerator can be zero but not negative in real numbers. The denominator must always be positive.

Q2: How precise are the calculations?
A: Results are calculated with floating-point precision and rounded to 6 decimal places.

Q3: Can this be extended to other roots?
A: Yes, the same property holds for nth roots: \(\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}\).

Q4: Why is this property useful?
A: It simplifies complex fractions under roots and is essential for solving many algebraic equations.

Q5: What happens if denominator is zero?
A: Division by zero is undefined, so the calculator requires a positive denominator.