Question

To prove that 35√35 is irrational, assume the product is rational and set it equal to ​ abab ​, where b is not equal to 0. Isolating the radical gives 5√=a3b5=a3b . The right side of the equation is . Because the left side of the equation is , this is a contradiction. Therefore, the assumption is wrong, and the opposite of the assumption must be true.