Number Properties Puzzle – Challenge 5
This is a great mathematics critical thinking challenge for those who love math puzzles and challenges. Let's see if you can solve this math puzzle!

Challenge:
Number 4 is a perfect square number (2 × 2 = 4) and number 8 is a perfect cube number (2 × 2 × 2 = 8). How many positive perfect square numbers less than 2016 are also perfect cubes?
A- 2
B- 3
C- 4
D- 5
E- 10
The Absolute Best Book to Challenge Your Smart Student!

The correct answer is B.
Because there aren’t that many perfect squares less than 2016 that is also a perfect cube, let’s look for the smallest perfect square number. This happens to be number 1. It is a perfect square number (1 × 1 = 1) and a perfect cube number (1×1×1=1). To find the next positive perfect square number less than 2015 that is also a perfect cube, let’s take a look at number 2. \(2^{2} = 4\) is a perfect square and \(2^{3} = 8\) is a perfect cube number and \((2^{2})^{3} = 2^{6} = 64\), which is both a perfect square and cube number. Next perfect square and cube number with the base of 2 is \((2^{6})^{2} =2^{12} = 4096\), which is greater than 2016.
With the same method, \(3^{6} = 729\) is the next perfect square number and cube. \(4^{6} = 4096\) is a perfect square and cube number, but is bigger than 2016. Therefore, numbers 1, 64 and 729 are the perfect square and cube numbers less than 2016.
The Absolute Best Books to Ace Algebra
Related to This Article
More math articles
- How to Use a Protractor to Draw Angles
- Algebra Puzzle – Critical Thinking 13
- 6th Grade NYSE Math Practice Test Questions
- How to Find the Area and Circumference of Circles? (+FREE Worksheet!)
- SSAT Middle Level Math FREE Sample Practice Questions
- 3rd Grade Mathematics Worksheets: FREE & Printable
- A Parents’ Guide To Supporting Teens With Their Math Skills
- How is the GED Math Scored?
- How to Make Math Lessons More Engaging?
- How to Verify Inverse Functions by Composition?
What people say about "Number Properties Puzzle – Challenge 5 - Effortless Math: We Help Students Learn to LOVE Mathematics"?
No one replied yet.