What is the smallest number by which 256 must be multiplied to obtain a perfect cube?

see full answer

High-Paying Jobs That Even AI Can’t Replace — Through JEE/NEET

🎯 Hear from the experts why preparing for JEE/NEET today sets you up for future-proof, high-income careers tomorrow.

An Intiative by Sri Chaitanya

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

It is required to find the smallest number by which 256 must be multiplied to obtain a perfect cube.
Utilizing prime factorization and grouping the factors in triple form, express the given number as a product of prime factors.

256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 ⇒ 23 × 23 × 22

We see that the prime factor 2 does not appear in the group of triples.
So, we need one more 2 to make it a cube.
In order to create a perfect cube, 256 must be multiplied by the least number possible, which equals 2.
Therefore, option 2 is correct.

Watch 3-min video & get full concept clarity

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE

Ready to Test Your Skills?

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

Take Free Test

Get Expert Academic Guidance – Connect with a Counselor Today!

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Online Course for IIT JEE

Best Online Course for NEET

Best Online Course for CBSE