Question

Prove that root 3 is irrational and hence prove that root 3+ root 5 is irrational

Answer 1

Answer:

Let √3+√5 be a rational number. A rational number can be written in the form of p/q where p,q are integers. ... But this contradicts the fact that √5 is an irrational number. So,our supposition is false.

Answer 2

Let as assume on contrary that

√3 + √5

is a rational number.

Then there exists co - prime integers p and q such that

⇒ √3

is a rational number .

But this contradicts the fact that

√3

is irrational.

So, our assumption is wrong.

Hence,

√3 + √5

is irrational.