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The concept is fundamental to geometry. A square, with sides of one unit, has a diagonal of length = sqrt(2).

Pythagoras's theorem appears all over the place. If you have a doorway that is X units wide and Y units tall, then the widest object you can take through it is sqrt(X2 + Y2) units.

On a Cartesian plane (or even city blocks) the distance (as the crow flies) between two points that are X blocks apart North-to-South and Y blocks East-to-West is also sqrt(X2 + Y2) times the block size.

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Q: Why are square root functions important?
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