Natalie solved a problem comparing the square root of 2 and the cube root of 3. She showed that (the square root of 2)^6 equals 8, while (the cube root of 3)^6 equals 9. Therefore, the cube root of 3 is greater than the square root of 2.

1. Natalie’s Problem of the Week Solution

2. Let x = the square root of 2 which equals 2^1/2 and y = the cube root of 3 which equals 3^1/3. x^ 6 = (2^1/2)^6 = 2^3 = 8 y^ 6 = (3^1/3)6 = 3^2 = 9 As y^ 6 is greater than x^ 6 it follows that the cube root of 3 will be greater than the square root of 2.