A square is a cube

Number Theory Level pending

What 2-digit number, when squared, produces a number equal to the cube of its sum of digits?

1 solution

Danish Ahmed
Jan 10, 2015

If a number when squared is a cube, then the original number is also a cube.

The only two digit cubes are $27$ and $64$ .

$27^2 = 729$ and $(2 + 7)^3 = 729$

So $27$ is the answer.