Question

Write the lowest rationalising factor of :

$15-3\sqrt{2}$ is $m+\sqrt{2}$
$m$ is

Answer 1

The least rationalizing factor will be of the form $a\sqrt{2}+b15-3\sqrt{2}\ast (a\sqrt{2}+b)=-a\ast 3\ast 2+15\ast b-3b\sqrt{2}+15a\sqrt{2}$
To be rational, $15a\sqrt{2}=3b\sqrt{2}15a=3b$
i.e, $a=1,b=5,\sqrt{2}+5$ is the least rationalizing factor