√72 is already a number — about 8.485. Simplifying it does not make it smaller or more exact; it rewrites it so that no perfect square is left trapped inside the radical. The whole method rests on one rule, √(ab) = √a · √b, and that rule has a picture: a square of area 72 is exactly thirty-six little squares of area 2, six of them across. Step through each example one line at a time and watch the square come apart.
The picture
Simplified form—
the part that escapes the part that stays inside
Try any radicand
272200
Simplify a radical, one line at a timepick an example below