Is the 2 square root of 5 rational or irrational why?

Answer 1

It is irrational.

The proof depends on the proof that sqrt(5) is irrational. However, judging by this question, I suggest that you are not yet ready for that proof.

So, assume that sqrt(5) is irrational. Any multiple of an irrrational number by a non-zero rational isirrational.

For suppose 2*sqrt(5) were rational

that is 2*sqrt(5) = p/q for some integers p and q, where q is nonzero.

then dividing both isdes by 2 gives sqrt(5) = p/(2q) where p and 2q are both integers and 2q in non-zero.

But that implies that sqrt(5) is rational!

That is a contradiction so 2*sqrt(5) cannot be rational.

Answer 2

The square root of 5 is an irrational number because it can't be expressed as a fraction