Question

prove 5 + 2 under root 3 is irrational​

Answer 1

To prove:

5 + 2√3 is irrational

Proof:

Let 5 + 2√3 be rational

So 5 + 2√3 = p/q where p and q are co- prime.

5 + 2√3 = p/q

2√3 = p/q - 5/1

=. p/q - 5q/q

√3 = p -5q

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2q

Here we know that √3 is irrational and the RHS is rational... So this is a contradiction against our assumption.....

Therefore 5 + 2√3 is irrational...

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