Question

Which of the following is both a perfect square and a perfect cube?

64
16
81
1,000

I know the answer is 64, but how? Can someone please explain me to me how to work this out?

Answer 1

Well the square root of 64 is 8, and the cube root of 64 is 4. They’re perfect whole numbers. We know 4 x 4 = 16 is a square from the fact above, and also because of what a square means. But we can go one step further. 4 x 16 = 64 is the product of two squares, so it is also a square. But you can also write it as 64 = 4 x 4 x 4, making it a cube.