Prove that frac{1}{sqrt{2}} is an irrational | vedclass

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(B) Assume that $\frac{1}{\sqrt{2}}$ is a rational number.Therefore,we can find two integers $a$ and $b$ $(b 
eq 0)$ such that $\frac{1}{\sqrt{2}} =

Vedclass · Accepted Answer

Irrational

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(B) Assume that $\frac{1}{\sqrt{2}}$ is a rational number.Therefore,we can find two integers $a$ and $b$ $(b 
eq 0)$ such that $\frac{1}{\sqrt{2}} = \frac{a}{b}$.By rearranging the terms,we get $\sqrt{2} = \frac{b}{a}$.Since $a$ and $b$ are integers,$\frac{b}{a}$ is a rational number.This implies that $\sqrt{2}$ is a rational number.However,this contradicts the established fact that $\sqrt{2}$ is an irrational number.Therefore,our initial assumption is false,and $\frac{1}{\sqrt{2}}$ must be an irrational number.

Prove that $\frac{1}{\sqrt{2}}$ is an irrational number.

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