Question

Is the square root of eight a rational or irrational number

Answer 1

$\bf \sqrt{8}\implies \sqrt{2\cdot 2\cdot 2}\implies \sqrt{2^2\cdot 2}\implies 2\sqrt{2}$

it just so happen that √2 is an irrational number, so any product with it as a factor, will yield an irrational number as well.



factoid:   Ancient Greeks were scared of irrational numbers, and they steered clear from √2.