Question

which integer is closest to $sqrt3{307}$?

Explanation:

Step1: Find nearby perfect cubes

$6^3 = 6 \times 6 \times 6 = 216$
$7^3 = 7 \times 7 \times 7 = 343$

Step2: Calculate differences to 307

$307 - 216 = 91$
$343 - 307 = 36$

Step3: Compare differences

36 < 91, so 307 is closer to $7^3$.

Answer:

7