Question

Prove that 5 - 2√3 is an irrational number.​

Answer 1

Answer:

we ca assume that 5-√3 is an irrational al number

Answer 2

$\huge\underline\mathcal\pink{Answer♡}$

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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,

5-2√3 = p/q

→  -2√3 = p/q -5

→  -2√3 = P-5q / 2

→  √3 = ( p- √a / 2a)

We know that ,

√3   is irrational .

√3   is irrational .And,  (r-5q / 2q) 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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