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!

Number Properties Puzzle – Challenge 5

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!

$11.99

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.

What people say about "Number Properties Puzzle - Challenge 5"?

No one replied yet.

Leave a Reply

X
30% OFF

Huge Discount!

30% OFF

Take It Now!

SAVE $5

It was $16.99 now it is $11.99