Rationalize sqrt(28) by separating the two factors (4 and 7), so you get:
sqrt(4*7)
which becomes:
sqrt(4) * sqrt(7)
and you can simplify the square root of 4 to:
2*sqrt(7) ------ ANS
[tex]\bf (2\sqrt{7}+\sqrt{27})(\sqrt{28}-3\sqrt{3})\implies (2\sqrt{7}+\sqrt{9\cdot 3})(\sqrt{4\cdot 7}-3\sqrt{3}) \\\\\\ (2\sqrt{7}+\sqrt{3^2\cdot 3})(\sqrt{2^2\cdot 7}-3\sqrt{3})\implies (2\sqrt{7}+3\sqrt{3})(2\sqrt{ 7}-3\sqrt{3})[/tex]
[tex]\bf \stackrel{\underline{2\sqrt{7}\times (2\sqrt{ 7}-3\sqrt{3})}}{(2\sqrt{7})^2-6\sqrt{21}}+\stackrel{\underline{3\sqrt{3}\times(2\sqrt{ 7}-3\sqrt{3})}}{6\sqrt{21}-(3\sqrt{3})^2}\implies (2^2\sqrt{7^2})-6\sqrt{21}+6\sqrt{21}-(3^2\sqrt{3^2}) \\\\\\ (4\cdot 7)-0-(9\cdot 3)\implies 28-27\implies \boxed{1}[/tex]
notice, you can always multiply polynomials like say (a+b)(c+d+e), by simply doing a(c+d+e) + b(c+d+e), then combine like-terms and simplify.
