Question

Write the lowest rationalising factor of :

$\sqrt{13}+3$ is $\sqrt{13}-m$
$m$ is

Answer 1

The least rationalizing factor will be of the form $a\sqrt{13}-b\sqrt{13}+3\ast (a\sqrt{13}-b)=a\ast 13+3\ast b+b\sqrt{13}-3a\sqrt{13}$ to be rational,
$b\sqrt{13}=3a\sqrt{13}b=3ai.e,a=1,b=3$,
{$\sqrt{13}-3$ is the least rationalizing factor }

Ans- $3$