INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

April 5, 2020

Perfect cubes | Algebra | AMC 8, 2018 | Problem 25

Try this beautiful problem from Algebra based on Perfect cubes from AMC-8, 2018, Problem -25.

Perfect Cubes | AMC-8, 2018| Problem 22

How many perfect cubes lie between $2^8+1$ and $2^{18}+1$, inclusive?

  • 55
  • 60
  • 58

Key Concepts




Check the Answer


AMC-8, 2018 problem 25

Challenges and Thrills in Pre College Mathematics

Try with Hints

Find the vale 0f \(2^8+1\) and \(2^{18} +1\)

Can you now finish the problem ..........

Find the lest and largest cubes betwwen \(2^8+1\) and \(2^{18} +1\)

can you finish the problem........

The value of \(2^8+1=257\)

Now less than 257 the perfect cube is \(6^3\)=216 and \(7^3=343\),which is greater than 257

Now \(2^{18}=(2^6)^3=(64)^3\) which will be the largrst cube less than \(2^{18 }+1\)

Hece the required number of cubes is 64-7+1=58

Subscribe to Cheenta at Youtube

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.