Question

prove that 2+2√3 Is irrational

Note 4 is not the answer ​

Answer 1

Answer:

2+2√3 is definitely an irrational number.

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

Hope it helps. Thank You!

Answer 2

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