Question

If $7-\sqrt{7}$ is $m+\sqrt{7}$, then $m$ is

Answer 1

The least rationalizing factor will be of the form $a\sqrt{7}+b$

$(7-\sqrt{7})\times (a\sqrt{7}+b)=-a\times 7+7\times b-b\sqrt{7}+7a\sqrt{7}$

To be rational, $b\sqrt{7}=7a\sqrt{7}$

$b=7a$

i.e, $a=1,b=7$

$\sqrt{7}+7$ is the least rationalizing factor.