Question

Prove that 2+√3 is Irrational number.​

Answer 1

Step-by-step explanation:

 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

The value of root3 is 1.732.... wherein the numbers after the decimal don't repeat, therefore 2 + root3 is irrational
The rational number is either finite after the decimal or infinite but repeat in certain sets (like 3.333... or 1.575757...)