Question

prove that 1 by root 2 is an irrational number​

Answer 1

Answer:

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Answer 2

AnswEr:

Let us Consider that $\sf\dfrac{\:\:1}{\sqrt{2}}$ is an rational number.

Therefore, it can be written in the form of $\sf\dfrac{a}{b}$ where a & b are co - Primes and b is not Equal to zero.

Such that,

$:\implies\sf\: \dfrac{\:\:1}{\sqrt{2}} = \dfrac{a}{b}$

$:\implies\sf\: \sqrt{2} = \dfrac{a}{b}$

Here, we can see that $\sf\dfrac{a}{b}$ is an irrational number and is equal to $\sf\sqrt{2}$.

It arises contradiction because of our wrong assumption that $\sf\sqrt{2}$ is rational.

$\bold{\underline{\sf{\red{Hence,\dfrac{\:\:1}{\sqrt{2}} \: is \: an \: irrational\: number.}}}}$

$\rule{150}2$