Floor of Root of Floor equals Floor of Root

Theorem
Let $x \in \R$ be a real number.

Let $\left \lfloor {x}\right \rfloor$ denote the floor of $x$.

Then:
 * $\displaystyle \left \lfloor {\sqrt {\left \lfloor {x}\right \rfloor} }\right \rfloor = \left \lfloor {\sqrt x}\right \rfloor$

Also see

 * Ceiling of Root of Ceiling equals Ceiling of Root