2 answers? maybe 2 different forms?
remember that [tex]a^\frac{m}{n}=\sqrt[n]{a^m}[/tex]
also, that [tex]\sqrt{ab}=(\sqrt{a})(\sqrt{b})[/tex]
and [tex]\sqrt{a^2}=a[/tex]
so factor each
75=3*5*5
18=2*3*3
27=3*3*3
[tex]\sqrt{75}+\sqrt{18}-\sqrt{27}=[/tex]
[tex]\sqrt{(3)(5)(5)}+\sqrt{(2)(3)(3)}-\sqrt{(3)(3)(3)}=[/tex]
[tex](\sqrt{3})(\sqrt{5})(\sqrt{5})+(\sqrt{2})(\sqrt{3})(\sqrt{3})-(\sqrt{3})(\sqrt{3})(\sqrt{3})=[/tex]
[tex](\sqrt{3})(5)+(\sqrt{2})(3)-(3)(\sqrt{3})=[/tex]
[tex]5\sqrt{3}-3\sqrt{3}+3\sqrt{2}=[/tex]
[tex]2\sqrt{3}+3\sqrt{2}[/tex]
not sure what the other solution is
you could go to back and factor out the √3 back there to get
[tex](\sqrt{3})(2+\sqrt{6})[/tex] but that's all I can see
