If the length of an edge in a cube is 3√3, what is the length of the longest diagonal?

Question: If the length of an edge in a cube is 3√3, what is the length of the longest diagonal?

Solution:
Let the length of an edge of the cube be a.
Given that, a = 3√3

We know, the length of the longest diagonal of a cube is given by the formula: d = a√3
∴ d = (3√3) × √3
⇒ d = 3 × (√3 × √3)
⇒ d = 3 × 3
∴ d = 9

∴ The length of the longest diagonal is 9.