1. What is Square Root of Fraction?

The square root of a fraction equals the fraction of the square roots of numerator and denominator. This property simplifies calculations involving roots of fractions.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

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

Explanation: The calculator shows both the direct calculation (√(a/b)) and the equivalent fraction (√a/√b) to demonstrate the mathematical equality.

3. Mathematical Proof

Proof: \[ \left( \frac{\sqrt{a}}{\sqrt{b}} \right)^2 = \frac{(\sqrt{a})^2}{(\sqrt{b})^2} = \frac{a}{b} \] Therefore, \[ \frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}} \]

4. Using the Calculator

Tips: Enter positive values for numerator (≥0) and denominator (>0). The denominator cannot be zero.

5. Frequently Asked Questions (FAQ)

Q1: Does this work for cube roots or other roots?
A: Yes, the same principle applies: ∛(a/b) = ∛a/∛b, and generally ⁿ√(a/b) = ⁿ√a/ⁿ√b for any positive integer n.

Q2: What if numerator or denominator is negative?
A: Numerator can be zero but not negative (in real numbers). Denominator must always be positive.

Q3: Why are there two results shown?
A: To demonstrate that both methods of calculation give identical results, verifying the mathematical property.

Q4: Can this be used for complex numbers?
A: With complex numbers, additional considerations are needed for principal roots, but the fundamental property holds.

Q5: How precise are the calculations?
A: Results are rounded to 6 decimal places for readability while maintaining practical accuracy.