so we want
a^2 = b^3
a = b^(3/2) or (√b)^3
so pick b = a perfect square,
e.g. b = 4 , then a = 8
so 8^2 = 4^3 = 64
let b = 9 , a = 27
9^3 = 27^2 = 729
let b = 16 , then a = 64
16^3 = 64^2 = 4096
let b = 25 , a = 125
25^3 = 125^2 = 15625
So the first few numbers with that property are:
64 , 729 . 4096 , 15625
As you can see, we can form as many of these as we want, there would be an infinite number of them.
What is the first natural number that is a perfect square and a perfect cube? Can you find the second? The third? Explain.
2 answers
Ok thank you. I understand now.