Question

Prove that 2+√3 is irrational

Answer 1

 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:

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

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

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