Question

# Prove that $$\sqrt {5}$$ is an irrational number.

Solution

## Let us assume that $$√5$$ is a rational number.we know that the rational numbers are in the form of p/q form where p,q are coprime numbers.so, $$\sqrt5 = \dfrac{p}{q}$$    $$p = \sqrt(5)q$$we know that 'p' is a rational number. so $$\sqrt(5)$$q must be rational since it equals to pbut it doesnt occurs with $$\sqrt(5)q$$ since its not an integertherefore, p is not equal to $$\sqrt(5)q$$this contradicts the fact that $$\sqrt(5)$$ is an irrational numberhence our assumption is wrong and $$\sqrt(5)$$ is an irrational numberMathematics

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