Q. 23.8( 366 Votes )

Prove that is irrational.

Answer :

To Prove: 3 + 2√5 is irrational
Proof:

Let
is rational.

A number is said to be rational if it can be expressed in the form p/q where q ≠ 0

Therefore,

We can find two integers p & q where, (q ≠ 0) such that

Since p and q are integers,   will also be rational and therefore, is rational.


We know that √5 is irrational but according to above statement it has to be rational

So, both the comments are contradictory,

Hence, the number should have been irrational to make the statement correct.

Therefore, is irrational

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