Question

Prove that 1/2+root 3 is an irrational number..

Answer 1

To prove this first we have to prove that root 3 is irrational number .
From above we proved that root 3 is irrational
so 1/2+root 3 is also irrational

Answer 2

Step-by-step explanation:

Correct Question:-

Prove that $\sf\; \frac{\;\; 1}{\sqrt{2}} + \sqrt{3}$ is an irrational number.

AnswEr:-

Let us assume that $\sf\; \dfrac{\;\;1}{\sqrt{2}} + \sqrt{3}$ is an rational number.

So, it can be written in the form of $\sf\dfrac{p}{q}$

Where p and q are Integers.

Such that,

$:\implies\sf\; \dfrac{\;\;1}{\sqrt{2}} + \sqrt{3} = \dfrac{p}{q}$

$:\implies\sf\sqrt{3} = \dfrac{p}{q} - \dfrac{1}{2}$

$:\implies\sf\sqrt{3} = \dfrac{2p - q}{2q}$

Here, we can see that $\sf\dfrac{2p - q}{2q}$ is an rational number but $\sf\sqrt{3}$ is an irrational number.

It arises contradiction because of our wrong assumption.

Hence $\sf\sqrt{3}$ is an irrational number.

$\rule{150}3$