\(\sqrt{2a}-\sqrt{18^3}+4\sqrt{\dfrac{a}{2}}=\sqrt{2}.\sqrt{a}-54\sqrt{2}+2\sqrt{2}.\sqrt{a}=3\sqrt{2}.\sqrt{a}-54\sqrt{2}\)
\(\sqrt{\dfrac{a}{1+2b+b^2}}.\sqrt{\dfrac{4a+8ab+4ab^2}{225}}=\sqrt{\dfrac{a}{\left(b+1\right)^2}}.\sqrt{\dfrac{4a\left(1+2b+b^2\right)}{225}}=\dfrac{\sqrt{a}}{\left|b+1\right|}.\dfrac{\sqrt{4a\left(b+1\right)^2}}{15}=\dfrac{\sqrt{a}}{\left|b+1\right|}.\dfrac{2\sqrt{a}\left|b+1\right|}{15}=\dfrac{2a}{15}\)