Square Root Simplifier

About this calculator

Simplifying a square root means rewriting it as a coefficient times the smallest possible radical, by pulling out any perfect-square factors: √72 becomes 6√2 because 72 = 36 × 2 and 36 is a perfect square. The value doesn’t change — 6√2 and √72 are the exact same number — but the simplified form is far easier to work with by hand.

Simplified radicals are the expected answer format in algebra and geometry classes, since unsimplified roots make it much harder to combine like terms (√8 + √18 doesn’t obviously simplify, but 2√2 + 3√2 = 5√2 does), rationalize denominators, or apply the quadratic formula cleanly when the discriminant isn’t a perfect square. The same factoring technique is also the basis for simplifying radical expressions in trigonometry (exact values like √3/2) and for reducing surds in physics formulas.

Enter any number under the radical and this calculator factors out the largest perfect square automatically, showing you the simplified coefficient-and-radical form along with the decimal approximation.