Comparison of cube roots: Which is greater, ∛8 or ∛1000?

Introduction / Context:
Estimating cube roots of perfect cubes is straightforward and useful in quick comparisons.

Given Data / Assumptions:
Compare ∛8 and ∛1000.

Concept / Approach:
Recognize that 8 = 2^3 and 1000 = 10^3. Then cube roots are exact integers.

Step-by-Step Solution:
∛8 = 2.∛1000 = 10.Therefore, ∛1000 > ∛8.

Verification / Alternative check:
Obvious by comparing 2 and 10.

Why Other Options Are Wrong:
∛8 is smaller; equality does not hold.

Common Pitfalls:
Confusing square roots with cube roots.

Final Answer:
∛1000