Question

prove that 2 +√3 is
irrational number​

Answer 1

Answer:

let us assume 2+√3 as rational.

⇒2+√3=a/b

∴2-a/b=-√3 or √3=a/b-2

⇒√3=a/b-2

√3=a-2b/b

∵a and b are positive integers  

∴a-2b/b is rational

⇒√3 is rational

but we know that √3 is irrational  

∴⇒2+√3 is irrational

Answer 2

Answer:

2+√3 is an irrational number

Step-by-step explanation:

Let us assume that 2+√3 is an rational number, then it can be written in the form p/q

2+√3=p/q (rational no)

√3= p-2/q (rational no)

√3=p-2q/q

This contradict the fact the fact that 2+√3 is a irrational number

therefore our assumption is wrong

(no-number)