Question

Prove that 2 -
$\sqrt{3}$
is irrational. When it is given
$\sqrt{3}$
is irrational. ​

Answer 1

Answer:

It is irrational ...by the method of contadiction

Step-by-step explanation:

you must have hear a moral that better alone than a bad conpany ...so ...root 3 is irrational and 2 is rational ....put rational no. as good boy and irrational ...as bad ...so every bad guy can change a good one ...always remember ..that bad and bad ....can be good but every bad guy changes a good one...ao when a rational no. comes in the company of irrationals ...it becomes irrational

Answer 2

To prove that 2 - √3 is irrational, when √3 is given irrational.

Let us consider 2 - √3 is rational.

So it can be written as p/q, because any rational number can be written in the form of p/q.

$2 - \sqrt{3} = \frac{p}{q} \\ = > - \sqrt{3} = \frac{p}{q} - 2 \\ = > - \sqrt{3} = \frac{p - 2q}{q} \\ = > - \sqrt{3} \times - 1 = \frac{(p - 2q) \times ( - 1)}{q} \\ = > \sqrt{3} = \frac{ - p + 2q}{q}$

So -p+2q/q is rational, because it is written in the form of p/q. But √3 is irrational. so our consideration was wrong and 2-√3 is a irrational number.

hope it helps.