Answer
$\sqrt{3}$
Work Step by Step
Extracting the factors that are perfect powers of the index, the given expression simplifies to
\begin{array}{l}\require{cancel}
2\sqrt{75}-9\sqrt{3}
\\\\=
2\sqrt{25\cdot3}-9\sqrt{3}
\\\\=
2\sqrt{(5)^2\cdot3}-9\sqrt{3}
\\\\=
2\cdot5\sqrt{3}-9\sqrt{3}
\\\\=
10\sqrt{3}-9\sqrt{3}
.\end{array}
By combining like radicals, the given expression simplifies to
\begin{array}{l}\require{cancel}
10\sqrt{3}-9\sqrt{3}
\\\\=
(10-9)\sqrt{3}
\\\\=
1\sqrt{3}
\\\\=
\sqrt{3}
.\end{array}
