Question

find two irrational number between root2 and root3

Answer 1

Take a number between 2 and 3,which is a rational number. Clearly 2.25, i.e.,
$(1.5) {}^{2} is \: \: a \: number.$
$therefore \: \: 2 < ( {1.5})^{2} < 3 \: \: hence \: \sqrt{2} < 1.5 < \sqrt{3. }$
$therefore \: 1.5 \: is \: a \: rationl \: number \: between \: \sqrt{2 \: \: } and \: \sqrt{3} .$
Nótë : 2.56,2.89 are also perfect squares of rational numbers lying between 2&3 .so, 1.6&1.7 are also rational number lying between root2 & root3.