Question

Given that √3 is irrational, prove that 5 + 2√3 is an irrational number.

Answer 1

Answer:

To prove:

5 - 2√3  is irrational.

Assumption:

Let us assume 5 - 2√3 to be " a " and it is rational.

Proof,

As, 5 - 2√3 Is rational it can be written in the form of p/q where q ≠ 0.

(p , q are coprime) 

Then,

 

→  

→  

→  

We know that ,

√3   is irrational .

And,                is rational.

We know that ,

Irrational  ≠  rational..

So, we contradict the statement that  5 - 2 √ 3  is rational.

Therefore 5 - 2√3 is an irrational number

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Step-by-step explanation: