Exakt Rotförenklingslösare för Hypotenusa
Compute the exact hypotenuse length in simplified radical form without losing precision to rounding decimals. Our specialized tool extends the main Pythagoras equation solver with prime factorization, largest perfect square extraction, and a complete 5-step symbolic derivation.
Right Triangle Legs
Enter a positive length for Leg a.
Enter a positive length for Leg b.
Decimal Value: 6.7082
- 1Formula
c = √(a² + b²)a² + b² = c² ⇒ c = √(a² + b²)Start with the Pythagorean Theorem equating the sum of the squared legs to the squared hypotenuse.
- 2Substitution
c = √(6² + 3²)c = √(36 + 9) = √(45)Square Leg a (6) and Leg b (3), then sum both terms under the radical.
- 3Square Rooting
√(45) ≈ 6.7082√45 ≈ 6.7082Evaluate the principal square root. To retain full symbolic precision instead of a rounded decimal, simplify the radical next.
- 4Prime Factorization
45 = 3 × 3 × 5Largest square factor: 9 (3²)Factor 45 into primes (3 × 3 × 5) and group repeated prime pairs to find the largest perfect square factor (9).
- 5Final Extraction
√45 = √(9 × 5) = √9 · √5 = 3√5c = 3√5 (Decimal: 6.7082)Extract √9 = 3 outside the radical while keeping the square-free factor 5 inside.