Question

prove that root 3 is irrational​

Answer 1

Answer:

Step-by-step explanation:

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Answer 2

Let $\sqrt {3}$be a rational number.

then,

$\sqrt{3} = \frac{p}{q} \\ \\ \sqrt{3} q = p \\ \: \frac{p}{ \sqrt{3} } = q \\ \\ = > \frac{ \sqrt{3} p}{ \frac{p}{ \sqrt{3} } } = \frac{( \sqrt{3}p )( \sqrt{3} )}{p} = 3$

Here, $\frac{p}{q} = 3$. But, By the rule of rationality, the number being in form of $\frac{p}{q}$ should be co-primes i.e. their common factor can't be any number except 1.

Hence, Our assumption that $\sqrt{3}$ is a rational Number. Thus, It is proved that $\sqrt{3}$ is an irrational number.