Question

Prove that 3/√2 is an irrational number.

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Answer 1

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Let, 3/√2 be a rational number which can be written in the form of p/q where p and q are co-prime and q ≠ 0.

$\therefore \: \frac{3}{ \sqrt{2} } \: = \: \frac{p}{q}$

$\implies \: \sqrt{2} p \: = \: 3q$

$\implies \: \sqrt{2 } \: = \: \frac{3p}{q}$

As we can see this is in the form of p/q

Therefore, p/q is a rational number.

Therefore, 3q/p is a rational number.

Therefore, √2 is a rational number.

But it contradict the fact that √2 is rational.

Hence, √2 is an irrational number.

Therefore, 3/√2 is an irrational no.

Answer 2

Hope it helps you...‼️✌️