Question

Prove that 3+5√3 is irrational

Answer 1

Here is your answer user.

Answer 2

Answer:

let us assume,to the contrary, that 3+5 root 3 is rational

i.e. we can find co prime a & b (b not equals to 0) such that 3+5root 3= a

b

5root3 = a-3

b

5root3 = a-3b

b

root 3= a-3b

5b

hence, a&b are integers,we get a-3b

5b

as rational no., so, root 3 is rational but this contridicts the fact that root 3 is irrational.... this contridiction has arisen due to our wrong assumption that 3+5root3 is rational

hence, 3+5root3 is irrational

hope you find it useful