Question

prove that 1/√2 is ir rational​

Answer 1

Correct Question:-

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

Solution:-

Let us assume that $\sf\frac{\;\;\;1}{\sqrt{2}}$ is rational number.

Then, we can find co - prime a and b where (b ≠ 0).

Such that $\sf \frac {\;\;\;1}{\sqrt{2}} \; = \; \frac{a}{b}$

Rearranging we get,

$\sf\sqrt{2} \;= \; \frac{a}{b}$

Since, a and b are two positive integers, thus $\sf\sqrt{2}$ is irrational number, which contradiction the fact that $\sf\sqrt{2}$ irrational number.

Hence, We conclude that $\sf\frac{\; \;\;1\;}{\sqrt{2}}$ is irrational.

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Rational number is the number which can be expressed in the form of $\sf\frac{p}{q}$. Here, (q ≠ 0) since q may be equal to 1.

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