Question

In the Venn diagram, consider U = {whole numbers 1 – 100}.

Let A represent numbers that are perfect squares, B represent numbers that are perfect cubes, and C represent numbers that are perfect fourths, or numbers with a fourth root that is an integer.



Circles A, B, and C overlap.

Which number(s) satisfy A ∩ C?

16, 81
1, 16, 81
1, 4, 9, 16, 25, 36, 49, 81, 100
1, 4, 9, 16, 25, 36, 49, 64, 81, 100

Answer 1

A ∩ C are numbers that are both perfect squares and perfect fourth powers. Every fourth power k^4 is a square ((k^2)^2), so A ∩ C = C. The fourth powers ≤100 are 1^4=1, 2^4=16, 3^4=81.

Answer: 1, 16, 81.