1. What is Square Root of Fractions?

The square root of a fraction equals the fraction of the square roots of numerator and denominator. This property simplifies complex fractional expressions under square roots.

2. How Does the Calculator Work?

The calculator uses the mathematical property:

Where:

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

Explanation: This property holds true for all non-negative real numbers in the numerator and positive real numbers in the denominator.

3. Mathematical Explanation

Details: The square root of a fraction can be separated into the fraction of square roots because (√a/√b)² = (√a)²/(√b)² = a/b, proving the original relationship.

4. Using the Calculator

Tips: Enter any non-negative numerator and positive denominator. The calculator will show both forms of the result: the square root of the simplified fraction and the fraction of square roots.

5. Frequently Asked Questions (FAQ)

Q1: Can the numerator be zero?
A: Yes, √(0/b) = 0/√b = 0 for any positive denominator b.

Q2: Why can't the denominator be zero?
A: Division by zero is undefined in mathematics, and square root of zero in the denominator would make the expression undefined.

Q3: Does this work with complex numbers?
A: The calculator handles real numbers only. Complex numbers require different handling of square roots.

Q4: Can this be extended to other roots?
A: Yes, the same property applies to nth roots: ⁿ√(a/b) = ⁿ√a/ⁿ√b.

Q5: How precise are the results?
A: Results are calculated with floating point precision (about 15-16 significant digits).