Square Root Simplifier

Simplify square roots by finding perfect-square factors and moving factor pairs outside the radical.

RADICALS

LOCAL NO DATA SENT

RADICAL WORKBENCHPERFECT-SQUARE FACTORS / SIMPLIFIED RADICAL / SHOW THE WORK

RADICANDENTER A WHOLE NUMBER

NUMBER UNDER THE SQUARE ROOT

Look for pairs of matching prime factors. Each pair can move outside the square root as one factor.

ANSWER—The remaining factor stays under the radical when it has no perfect-square factor greater than 1.

√(a² × b) = a√b — a perfect-square factor can be pulled outside the radical.

STEPSPERFECT SQUARE → SPLIT RADICAL → SIMPLIFY

READYEnter a whole number under the radical.

LOCAL TOOL: Radical simplification stays entirely in your browser.

FIELD NOTE / 048

Square roots simplify when the radicand contains perfect-square factors.

Pairs of matching prime factors form a square. Move one factor from each pair outside the radical and leave any unpaired factors inside.