a) $\sqrt{a^4.(3-a)^2}=\sqrt{a^4}.\sqrt{(3-a)^2}=a^2.(3-a)=3a^2-a^3$
b) $\dfrac{1}{a-b}.\sqrt{a^4.(a-b)^2}=\dfrac{1}{a-b}.\sqrt{a^4}.\sqrt{(a-b)^2}$
$=\dfrac{1}{a-b}.a^2.(a-b)$
$=\dfrac{a^2.(a-b)}{a-b}=a^2$
c) $\sqrt{\dfrac{2a}{3}}.\sqrt{\dfrac{3a}{8}}$
$=\sqrt{\dfrac{2a}{3}.\dfrac{3a}{8}}$
$=\sqrt{\dfrac{6a^2}{24}}$
$=\sqrt{\dfrac{a^2}{4}}=\dfrac{a}{4}$
d) $\sqrt{5a}.\sqrt{45a}=\sqrt{5a.45a}=\sqrt{225a^2}$
$=\sqrt{225}.\sqrt{a^2}=15a$
e) $\sqrt{\dfrac{27.(a-3)^2}{48}}$
$=\sqrt{\dfrac{9.(a-3)^2}{16}}$
$=\dfrac{\sqrt{9.(a-3)^2}}{\sqrt{16}}$
$=\dfrac{3.(a-3)}{4}$
$=\dfrac{3a-9}{4}$
