Question

state whether the number (root 2-root3)(root 2-root 3) is rational or irrational justify

Answer 1

this is irrational no.
hope this help you

Answer 2

$( \sqrt{2} - \sqrt{3} )( \sqrt{2} - \sqrt{3} ) \\ = {( \sqrt{2 } - \sqrt{3} ) }^{2} \\ = (\sqrt{2} ) ^{2} + {( \sqrt{3} )}^{2} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: - 2( \sqrt{2} )( \sqrt{3} ) \\ = 2 + 3 + 2\sqrt{6}$
it is irrational number