Question

prove that 3root + 2root is an irrational number

Answer 1

in a, b are integers, a square + b square/ 2ab is rational and so root 3 is rational.
this contradicts the fact that root 3 is irrational.
hence root 2 + root 3 is an irrational..

Answer 2

Solution is in the following image.
Hope it helps.