Question

which integer is closest to \\(\sqrt3{118}\\)?

Explanation:

Step1: Find nearby perfect cubes

$4^3 = 64$, $5^3 = 125$

Step2: Compare distances to 118

Distance to $4^3$: $118 - 64 = 54$
Distance to $5^3$: $125 - 118 = 7$

Step3: Identify closer integer

7 < 54, so 5 is closer.

Answer:

5