Ceiling of Root of Ceiling equals Ceiling of Root

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

Let $\left \lceil {x}\right \rceil$ denote the ceiling of $x$.

Then:
 * $\displaystyle \left \lceil {\sqrt {\left \lceil {x}\right \rceil} }\right \rceil = \left \lceil {\sqrt x}\right \rceil$

Also see

 * Floor of Root of Floor equals Floor of Root