Question

show that 2√3 is irrational ​

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

Step-by-step explanation:

Answer 2

Answer:

We can prove it by contradictory method..

We assume that 2 + √3 is a rational number.

=> 2 + √3 = p/q , where p & q are integers, ‘q’ not = 0.

=> √3 = (p/q) - 2

=> √3 = (p - 2q)/ q ………… (1)

=> here, LHS √3 is an irrational number.

But RHS is a rational number.. Reason- the difference of 2 integers is always an integer. So the numerator (p- 2q) is an integer.

& the denominator ‘q’ is an integer.&‘q’ not = 0

This way, all conditions of a rational number are satisfied.

=> RHS (p- 2q)/q is a rational number.

But , LHS is an irrational.

=> LHS of….. (1) is not = RHS.

=> Our assumption, that 2 + √3 is a rational number, is incorrect..

=> 2 + √3 is an irrational number

Step-by-step explanation: