Question

Prove that 5+2√3 is irrational.

Answer 1

Hey friend!!!?

assume that 5+2 root 3 is rational

5+2 root 3 = a/b , where a and b are integers .

2 root 3 = a/b - 5

2 root 3 = ab - 5

2 root 3 = a/b - 5b/b

root 3 = (a-5b) / 2b

we know that a, b , 2 and 5 are integers and they are also rational

therefore root 3 will be rational

but we know that root 3 is irrational
there is a contradiction

so,

5 + 2 root 3 is an irrational number__proved

hope u found it useful ^_^