Question

please give me region p for p for
$p + \sqrt{3}$
is irrational

Answer 1

Hey there !!

Let p + √3 be rational.

p + √3 = a / b , where a and b are integers and b ≠ 0

√3 = a / b – p

√3 = ( a – pb ) / b

Since, ( a – pb ) / b is rational. so √3 is also rational.

But this contradicts the fact that √3 is irrational.

Our incorrect consumption is wrong.

So, we conclude that p + √3 is irrational.