Question

prove that under root 3 + 5 under root 2 is an irrational number

Answer 1

3 is a rational number and 5 under root 2 is an irrational number
so by property that addition of rational and irrational is always irrational
hence it is proved :)

Answer 2

Let us assume that 5+2√3 is rational

5+2√3 = p/q ( where p and q are co prime)

2√3 = p/q-5

2√3 = p-5q/q

√3 = p-5q/2q

now p , 5 , 2 and q are integers 

∴ p-5q/2q is rational

∴ √3 is rational

but we
know that √3 is irrational . This is a contradiction which has arisen due to our wrong assumption.

∴ 5+2√3 is irrational

Mark as brainleist....