Radical Simplifier

Simplifying a radical means rewriting it so the number under the root sign has no perfect square (or perfect cube, etc.) factors remaining. For example, √72 simplifies to 6√2, because 72 = 36 × 2, and √36 = 6. The goal is to pull as much as possible outside the radical sign.

The tool finds the prime factorization of your radicand. It then identifies which prime factors appear enough times to be pulled out of the root (groups of 2 for square roots, groups of 3 for cube roots, etc.). The extracted portion becomes the coefficient outside the root, and any leftover factors stay inside.

First, find perfect square factors of the radicand. For example, √48 = √(16 × 3) = √16 × √3 = 4√3. Knowing your square numbers (4, 9, 16, 25, 36, 49…) helps you spot these factors quickly. For higher roots, look for perfect cubes or fourth powers instead.

The radicand is the number or expression placed under the radical sign (√). In √72, the radicand is 72. In ∛125, the radicand is 125. This is the value the tool simplifies.

Yes. Use the Root Degree selector to choose square root (2), cube root (3), fourth root (4), or fifth root (5). The simplification logic adjusts automatically — for cube roots it looks for groups of three identical prime factors to extract, and so on.

If the radicand has no perfect square (or higher power) factors, it is already fully simplified. The tool will show a coefficient of 1 and the original number as the remaining radicand, confirming it cannot be reduced further.

When you enable 'Show Prime Factorization', the table lists each prime factor, how many times it appears, how many copies were extracted from the root, and how many remain inside. This gives you a step-by-step view of exactly how the simplification was performed.

Simplified radicals are easier to compare, add, and subtract. Most math courses and standardized tests require answers in simplified radical form. Rationalized and simplified expressions are also less prone to arithmetic errors in further calculations.