Question

3 root 2 by 4 is an irrational number

Answer 1

$Hey\: There$ ‼
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Let 3√2 / 4 be a rational number.

3√2 / 4 = a / b , where a and b are co-prime and (b≠0).

3√2 = 4a / b

√2 = 4a / 3b

Since 4a / 3b is rational so, √2 is also rational.

But this contradicts the fact that √2 is irrational.
Therefore, our incorrect consumption is wrong.

So, we conclude that 3√2 / 4 is an irrational number.
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$Hope\: my \: ans.'s \: satisfactory.$

Answer 2

Heya !!

Here's your answer..⬇⬇
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➡ To Prove :- 3√2/4 is an irrational no.

➡ Proof :- Let 3√2/4 is rational no.

$\frac{3 \sqrt{2} }{4} = \frac{p}{q} \\ \\ 3 \sqrt{2} = \frac{4p}{q} \\ \\ \sqrt{2} = \frac{4p}{3q}$
irrational no. ≠ rational no.

√2 is an irrational no.
4p/3q is a rational no.

Hence our supposition is wrong.

3√2/4 is an irrational no.
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Hope it helps..
Thanks :)