# 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

- 4th Grade IAR Math Worksheets: FREE & Printable
- 3rd Grade PSSA Math Worksheets: FREE & Printable
- How to Measures of Dispersion?
- 5th Grade FSA Math Worksheets: FREE & Printable
- Top 10 3rd Grade ACT Aspire Math Practice Questions
- FREE 4th Grade MEAP Math Practice Test
- The Ultimate CHSPE Math Course (+FREE Worksheets & Tests)
- ACT Math: Test-Taking Strategies
- The Ultimate 7th Grade LEAP Math Course (+FREE Worksheets)
- 3rd Grade IAR Math Worksheets: FREE & Printable

## What people say about "Number Properties Puzzle – Challenge 5 - Effortless Math: We Help Students Learn to LOVE Mathematics"?

No one replied yet.