Answer
$-0.6$
Work Step by Step
Using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the given expression, $
(\sqrt{1.25}-\sqrt{1.8})(\sqrt{5}+\sqrt{0.2})
,$ is equivalent to
\begin{align*}
&
\sqrt{1.25}(\sqrt{5})+\sqrt{1.25}(\sqrt{0.2})-\sqrt{1.8}(\sqrt{5})-\sqrt{1.8}(\sqrt{0.2})
\\&=
\sqrt{1.25(5)}+\sqrt{1.25(0.2)}-\sqrt{1.8(5)}-\sqrt{1.8(0.2)}
\\&=
\sqrt{6.25}+\sqrt{.25}-\sqrt{9}-\sqrt{0.36}
\\&=
\sqrt{(2.5)^2}+\sqrt{(0.5)^2}-\sqrt{3^2}-\sqrt{(0.6)^2}
\\&=
2.5+0.5-3-0.6
\\&=
-0.6
.\end{align*}
Hence, the simplified form of the given expression is $
-0.6
$.
