Question

prove that the 1/root2 is irrational
I want full explanation and step by step solution please it urgent ​

Answer 1

Answer:

1/√2 is an irrational number because there is a rule that any rational number divided by an irrational number is always irrational.

Answer 2

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

Rational Numbers are in the form of p/q.

So,

$\huge\sf\pink{ \frac{p}{q} = \frac{1}{ \sqrt{2} }}$

So,

$\huge\sf\blue{\frac{q}{p} = \sqrt{2}}$

But, √2 is irrational.

So, 1/√2 is also irrational.

Hence, Proved.