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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.
Wiki User
∙ 9y ago
Wiki User
∙ 6y agoThe square root of 5 is an irrational number because it can't be expressed as a fraction
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