Question

Prove that $4+5\sqrt{3}$ is an irrational number.

Answer 1

An irrational number can be written as a decimal, but not as a fraction.

An irrational number has endless non-repeating digits to the right of the decimal point.

$4+5\sqrt{3}=4+5\left(\mathrm{1.732050.....}\right)=4+\mathrm{8.66025....}=\mathrm{12.66025...}$

As per definition $4+5\sqrt{3}$ is an irrational number