Which of the numbers is a perfect cube?

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

243

512

392

8640

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

The given numbers are 243, 512, 392, 8640.
Utilizing prime factorization, express the given number as a product of the factors in the triple form.
From option 1,

⇒ 243 = 3 × 3 × 3 × 3 × 3 = 33 × 32

From option 2,

⇒ 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 = 23 × 23 × 23

From option 3,

⇒ 392 = 2 × 2 × 2 × 7 × 7

From option 4,

⇒ 8640 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 ⇒ 23 × 23 × 33 × 5

The number 512 is a perfect cube since there are no factors in grouping (triples) that are left over.
Thus, 512 is the ideal cube.
Therefore, option 2 is correct.

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th