Question

show that 3 root 2 is an irrational number​

Answer 1

Let 3√2 be a rational number.

=> 3√2 = p/q (p and q are co primes)

=> √2 = p/3q

Since p and q are integers we get p/3q a rational number . So √2 is also a rational number. But this contradicts the fact that √2 is an irrational number . So our assumption is wrong . As a result 3√2 is an irrational number.

Answer 2

$let \: us \: assume \: that \: 3 \sqrt{2} is \: rational \: then \\ 3 \sqrt{2} = \frac{p}{q} \\ \sqrt{2} = \frac{p}{3q} \\ now \: \frac{p}{q} is \: rational \: then \: \frac{p}{3q} \: is \: also \: rational \: but \: it \: is \: wrong \: so \: our \: assumption \: is \: wrong \: so \: 3 \sqrt{2} \: is \: irrational$

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