Question

prove that 5 + 3√3is an irrational number,if it is given that √3 is an irrational number.

Answer 1

let us assume to ur contradiction that 5+3√3 is rational so it can be written as a/b where a and b are Co prime
so
5+3√3=a/b
3√3=a/b-5
3√3=(a-5b)/ b
√3=(a-5b) /3b
here a and b are Integers so √3 is rational.but it's given that √3 is irrational..this contradiction has arisen because of our wrong assumption.. so √3 is rational...