Question

20 + V3 is an irrational number​

Answer 1

$Let \: us \: assume \: that \: 20 + \sqrt{3} \: is \: a \: rational \: number$

There exist co - prime integers a and b ( b is not equal to 0 ) such that ,

$20 + \sqrt{3} = \frac{a}{b}$

$- > \sqrt{3} = \frac{a}{b} - 20$

$- > \sqrt{3} = \frac{a - 20b}{b}$

We know that a and b are co - prime numbers

$So \: \frac{a - 20b}{b} \: is \: rational \: number \: ...so \: \sqrt{3} is \: rational \: no.$

$But \: this \: contradicts \: the fact \: that \: \sqrt{3} \: is \: irrational$

So our assumption is wrong..

$20 + \sqrt{3} \: is \: irrational \: number$

I hope it helps u dear friend ^_^♡♡