Simplifying √200 into 10√2 is satisfying, but radical expressions — the full algebraic kind, with variables and operations — demand a bigger toolkit. The core moves stay the same: pull perfect squares out from under the root, combine like radicals, and rationalize any denominator. √(8x³) becomes √(4x² · 2x) = 2x√(2x), the variable version of the number game. Each move has a number-world analog students already know, which is why teachers introduce √(a×b) = √a × √b with numbers first: √(36 × 2) = 6√2 is the training ground for √(4x² · 2x) = 2x√(2x).

The variable twist is the absolute value subtlety: √(x²) = |x|, not x, because the square root is non-negative while x might not be — though most Algebra II classes assume positive variables and write 2x. Rationalizing denominators (turning 1/√2 into √2/2 by multiplying top and bottom by √2) completes the standard-form requirements. This calculator factors your radicand: enter it and read the square root, its integer part, the largest perfect-square factor, and the remaining factor — the complete anatomy of the simplification. The examples √72 = 6√2, √50 = 5√2, √200 = 10√2 show the pattern at three scales.

With the pre-filled defaults — Radicand (under the radical) 72 — the Simplify Radical Expressions returns √(radicand) 8.48528137, Integer part of √(radicand) 8, Largest perfect square factor 64, Remaining factor inside √ 1. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.