1. The problem statement, all variables and given/known data Which is larger, square root of 2 or cubed root of 3? Prove one is larger than the other without using decimal approximations for either number. 3. The attempt at a solution I attempted to solve this through the contradiction that they were even. If they are not even then obviously one has to be larger than the other. Assume sqrt(2) = cuberoot(3), which is the contradiction to our original problem. We can manipulate this expression using algebra to evaluate whether it is true or not. sqrt(2)^3 = cuberoot(3)^3 2*sqrt(2) = 3 sqrt(2)= 3/2 sqrt(2)^2 = (3/2)^2 2 = 9/4 This is our false statement! Since the two numbers are not equivalent, one must therefore be larger than the other number. Now I know they're not equal so one must be larger. Can I conclude from my algebra at the end that the cube root of 3 is larger?