Question

which integer is closest to $sqrt3{13}$?

Explanation:

Step1: Find nearby perfect cubes

$2^3 = 8$, $3^3 = 27$

Step2: Calculate differences to 13

$13 - 8 = 5$, $27 - 13 = 14$

Step3: Compare difference magnitudes

$5 < 14$, so 13 is closer to $2^3$

Answer:

2