Question

Check whether 46656 is a perfect cube or not.

Answer 1

By resolving 46656 into prime factor :


46656 = 2×2×2×2×2×2×3×3×3×3×3×3
By grouping the factors in triplets of equal factors,
46656 = (2×2×2)×(2×2×2)×(3×3×3)×(3×3×3)
Here, 46656 can be grouped into triplets of equal factors,
∴ $\sqrt[3]{346656}=2\times 2\times 3\times 3=36$
Hence, 46656 is cube of 36.