The correct option is
A True
Let us assume, to the contrary, that
3+2√5 is rational.
That is, we can find coprime integers a and b (b does not equal to 0) such that 3+2√5=ab.
Therefore, ab−3=2√5
a−3bb=2√5
a−3b2b=√5
a2b−32=√5
Since a and b are integers and rational, we get a2b−32 is rational, and so a−3b2b=√5 is rational.
But this contradicts the fact that √5 is irrational.
This contradiction has arisen because of our incorrect assumption that 3+2√5 is rational.
So, we conclude that 3+2√5 is irrational.