# This Floor Function Is Slippery!

**Algebra**Level 1

For all \(x \ge 0\), and \(x \in \mathbb {\text{R}}\), is it true that

\[ \left \lfloor \sqrt{\lfloor x \rfloor}\right \rfloor = \left \lfloor \sqrt{x} \right \rfloor \]

For all \(x \ge 0\), and \(x \in \mathbb {\text{R}}\), is it true that

\[ \left \lfloor \sqrt{\lfloor x \rfloor}\right \rfloor = \left \lfloor \sqrt{x} \right \rfloor \]

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