Flooring Cubes

Algebra Level 3

Determine the value of

(3+5)3 \left \lfloor ( 3 + \sqrt{5} ) ^3 \right \rfloor

Details and assumptions

Greatest Integer Function: x:RZ\lfloor x \rfloor: \mathbb{R} \rightarrow \mathbb{Z} refers to the greatest integer less than or equal to xx. For example 2.3=2\lfloor 2.3 \rfloor = 2 and 3.4=4\lfloor -3.4 \rfloor = -4.

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