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Prove that √12 is irrational

Answer»

Answer:

A rational number is what we can express as a fraction of two integers.

like \frac{p}{q}. If we could express \sqrt{12} as a fraction then it WOULD be a rational number. But we can't do it so it is irrational.

Step-by-step explanation:

Let's SAY . \sqrt{12} is rational.

so we could WRITE it as a fraction of two rational numbers \frac{p}{q}.

\sqrt{12} = \frac{p}{q}\\ (\sqrt{12})^2 = (\frac{p}{q})^2\\12 = \frac{p^2}{q^2}\\12q = \frac{p^2}{q} \\

look, p and q both are integers. so 12q would be also an INTEGER. but \frac{p^2}{q} can't be an integer as p is integer and q is also integer. so it would be a fraction .

so,12q \neq \frac {p^2}{q}

so \sqrt{12} can't be a rational number.

So it is obviously an irrational value.


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