Question

Prove that 2root 3+5 is an irrational no

Answer 1

Let assume that
$2 \sqrt{3} + 5$
is rational number.

Therefore,

$2 \sqrt{3} + 5 = \frac{a}{b} \\ \\ 2 \sqrt{3} = \frac{a}{b} - 5 \\ 2 \sqrt{3} = \frac{a - 5b}{b} \\ \\ \sqrt{3} = \frac{a - 5b}{2b}$

Here,

√3 is in the form of p/q which contradicts our fact that √3 is an irrational number.

Therefore, our assumption is wrong.

and the given number is an irrational number.