Question

If √ab is an irrational number, prove that √a+√b is irrational.

Answer 1

We know that if a number is said to be irrational then it is a non terminating anD non re-occuring . So if, it is said that under root a and under root b is irrational , then these variables are non terminating and non re-occuring.

Answer 2

Since, √a + √b are rational, So a and b are also rational. So, RHS of equation 2 is a rational number. But it is given that √(ab) is an irrational number. So, LHS of equation 2 is an irrational number.