Giventhat root 3 is an irrational prove that 5-2root3 is an irrational

1.	Giventhat root 3 is an irrational prove that 5-2root3 is an irrational
Answer» 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

Answer»

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

Discussion