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Simplifying a square root means factoring out the largest perfect square factor, leaving the smallest possible number under the radical. This tool simplifies √n for any non-negative integer n and shows the factorization used.
How it works
The largest perfect square that divides the radicand is found, then the square root is split using √(a×b) = √a × √b — the perfect square factor comes out of the radical as its own square root, leaving the remaining factor inside.
- Enter number under the square root.
- Click Calculate to see your results.
Examples
A classic simplification
√50 = √(25 × 2) = √25 × √2 = 5√2, since 25 is the largest perfect square factor of 50.
Who should use it
- Algebra coursework on simplifying radical expressions.
- Simplifying results from the quadratic formula or geometry (distance/area) calculations.
Industry applications
- Mathematics education (algebra and geometry)
Advantages
- Always finds the largest perfect square factor, giving the fully simplified form in one step.
- Shows the exact factorization used.
Limitations
- Only simplifies square roots — not cube roots or higher-order radicals.
Common mistakes to avoid
- Factoring out a perfect square factor that isn't the largest one available, leaving the result partially simplified (e.g. writing √50 as √2 × √25 without recognizing 5√2 is the final simplified form either way — but for numbers with multiple square factors, only the largest one gives full simplification in one step).
Best practices
- When simplifying by hand, check perfect squares from largest to smallest (4, 9, 16, 25, ...) up to the square root of the number, to find the biggest one that divides evenly on the first try.
Tips
- If a radicand is even, check for factors of 4 first (2² = 4) — it's often the quickest way to spot a perfect square factor.