Question

Prove that 3 + root 5 is irrational​

Answer 1

Answer:

Let us suppose 3+√5 is rational.

=>3+√5 is in the form of p/q where p and q are integers and q is not =0

=>√5=p/q-3

​=>√5=p-3q/q

as p, q and 3 are integers p-3q/3 is a rational number.

=>√5 is a rational number.

But we know that √5 is an irrational number.

This is an contradiction.

This contradiction has arisen because of our wrong assumption that 3+√5 is a rational number.

Hence 3+√5 is an irrational number.

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