Question

HELLo...
plz answer.....
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Answer 1

SOLUTION

=> Prove that 1/√2 is irrational.

we have to prove that $\sf\dfrac{1}{\sqrt{2}}$ is irrational.

Let us assume that $\sf\dfrac{1}{\sqrt{2}}$ is rational

So,

$\sf\dfrac{1}{\sqrt{2}}$ can be written in the form $\sf\dfrac{p}{q}$

where p and q (q ≠ 0) are co prime.

Hence,

$\sf\dfrac{1}{\sqrt{2}}$ = $\sf\dfrac{p}{q}$

Let us write the reciprocal of this..

$\sf\dfrac{q}{p}$ = $\sf\sqrt{2}$

But we already know that √2 is irrational..

and $\sf\dfrac{q}{p}$ is rational...

Since, rational ≠ irrational

.•. our assumption is incorrect

Hence, $\sf\dfrac{1}{\sqrt{2}}$ is irrational.

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