Question

The lowest rationalizing factor of :

$15-3\sqrt{2}$ is $5+\sqrt{m}$
The value of $m$ is

Answer 1

$Thelowestrationalizingfactorbeofthetypea+b\sqrt{2};(15-3\sqrt{2})(a+b\sqrt{2})=15a-3\ast b\ast 2+15\ast b\sqrt{2}-3a\sqrt{2};toberational,15b\sqrt{2}=3a\sqrt{2};\Rightarrow a=5b;fortheleastvalueofrationalizingfactor,b=1,a=5;i.e,5+\sqrt{2}Therefore:m=2$\\