Question

4. Prove that3 +2 √5is irrational.

Answer 1

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Solution:
To prove 3+2√5 is an irrational.
On the contray,let us assume that 3+2√5 is a rational number.
3+2√5=p/q(q not equals to 0)
2√5=p/q-3
p-3q/q
Here p,q being integers we can say that
p-3q/2q is a rational number.
This contradicts the fact that √5 is an irrational number.This us due to our assumption "3+2√5 is a rational number".
Hence,our assumption is wrong.
So the 3+2√5 is an irrational number.