a: \(A=\sqrt{27\cdot48\cdot\left(1-a^2\right)}\)
\(=\sqrt{3^3\cdot3\cdot16\cdot\left(1-a^2\right)}\)
\(=3^2\cdot4\cdot\sqrt{1-a^2}=36\sqrt{1-a^2}\)
b: a>b
=>a-b>0
\(B=\frac{1}{a-b}\cdot\sqrt{a^4\left(a-b\right)^2}\)
\(=\frac{1}{a-b}\cdot a^2\cdot\left|a-b\right|\)
\(=\frac{a^2\left(a-b\right)}{a-b}=a^2\)
c: \(C=\sqrt{5a}\cdot\sqrt{45a}-3a\)
\(=\sqrt{225a^2}-3a\)
=15a-3a
=12a
d: \(D=\left(3-a\right)^2-\sqrt{0,2}\cdot\sqrt{180a^2}\)
\(=\left(a-3\right)^2-\sqrt{180\cdot0,2}\cdot\left|a\right|\)
\(=\left(a-3\right)^2-6\left|a\right|\)
TH1: a>=0
=>\(D=\left(a-3\right)^2-6a\)
\(=a^2-6a+9-6a=a^2-12a+9\)
TH2: a<0
=>\(D=\left(a-3\right)^2+6a\)
\(=a^2-6a+9+6a=a^2+9\)
