Question

Prove that 3√5 is irrational.

Answer 1

Answer:

Let us assume that 3−

5

is a rational number

Then. there exist coprime integers p, q,q



=0 such that

3−

5

=

q

p

=>

5

=3−

q

p

Here, 3−

q

p

is a rational number, but

5

is a irrational number.

But, a irrational cannot be equal to a rational number.

This is a contradiction.

Thus, our assumption is wrong.

Therefore 3−

5

is an irrational number.

Answer 2

Answer:all rational numbers could be written in p/q form but it could not so it is irrational.