Answer
$\approx -6.9$
Work Step by Step
Using $\sqrt{3}=1.73$ and the properties of radicals, the value of the given expression, $
2\sqrt{27}-2\sqrt{75}
,$ to the nearest tenth, is
\begin{array}{l}\require{cancel}
2\sqrt{9\cdot3}-2\sqrt{25\cdot3}
\\\\=
2\sqrt{(3)^2\cdot3}-2\sqrt{(5)^2\cdot3}
\\\\=
2\cdot3\sqrt{3}-2\cdot5\sqrt{3}
\\\\=
6\sqrt{3}-10\sqrt{3}
\\\\=
-4\sqrt{3}
\\\\=
-4(1.73)
\\\\
\approx -6.9
.\end{array}
