a) \(\sqrt{5a^2}\)
\(=\sqrt{5}\cdot\sqrt{a^2}\)
\(=\left|a\right|\sqrt{5}\) (Do \(a\le0\Rightarrow\left|a\right|=-a\))
\(=-a\sqrt{5}\)
b) \(\sqrt{18a^2}\)
\(=\sqrt{18}\cdot\sqrt{a^2}\)
\(=\left|a\right|3\sqrt{2}\) (Do: \(a\ge0\Rightarrow\left|a\right|=a\))
\(=3a\sqrt{2}\)
c) \(\sqrt{-9b^3}\)
\(=\sqrt{3^2}\cdot\sqrt{-b}\cdot\sqrt{b^2}\)
\(=-3b\sqrt{-b}\) (Do: \(b\le0\Rightarrow\left|b\right|=-b\))
d) \(\sqrt{24a^4b^8}\)
\(=\sqrt{24}\cdot\sqrt{a^4}\cdot\sqrt{b^8}\)
\(=2\sqrt{6}\cdot\sqrt{\left(a^2\right)^2}\cdot\sqrt{\left(b^4\right)^2}\)
\(=2\sqrt{6}\cdot\left|a^2\right|\cdot\left|b^4\right|\)
\(=2a^2b^4\sqrt{6}\)
a: \(\sqrt{5a^2}=\sqrt{5}\cdot\left|a\right|=-a\sqrt{5}\)(Vì a<=0)
b: \(\sqrt{18a^2}=\sqrt{9a^2}\cdot\sqrt{2}\)
\(=3\cdot\left|a\right|\cdot\sqrt{2}\)
=3a*căn 2(a>0=0)
c: \(\sqrt{-9b^3}=\sqrt{b^2}\cdot\sqrt{-9b}\)
\(=3\sqrt{-b}\cdot\sqrt{b^2}\)
\(=-3b\sqrt{-b}\)(Vì b<=0)
d: \(\sqrt{24a^4b^8}=\sqrt{4a^4b^8}\cdot\sqrt{6}\)
\(=2a^2b^4\cdot\sqrt{6}\)
